Method for Evaluating Quality of Read Signal And Apparatus for Reading Information

ABSTRACT

A most probable path is selected from a number n (where n≧2) of paths of state transitions occurring from a first state S k−j  (where k≧3 and j≧2) at a time k−j into a second state S k  at a time k. The method includes the steps of detecting predetermined combinations of the first and second states S k−j  and S k  defining the n probable paths in a predetermined period j between the times k−j and k, and evaluating the reliability of a read signal, decoded in the period j, by |Pa−Pb|. Pa and Pb indicate the probabilities of state transition of first and second state transition paths in the period j. The first and second state transition paths are estimated to be the most probable and the second most probable, respectively, among the n probable paths defined by the combinations detected.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/198,604, filed Jul. 19, 2002, the disclosure of which is incorporatedherein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method for evaluating the quality ofa digital signal that has been read out from a storage medium and thendecoded by a maximum likelihood decoding technique, and also relates toan apparatus for reading information from a storage medium andperforming such quality evaluation on the read signal.

2. Description of the Related Art

Recently, various types of apparatuses (such as hard disk drive (HDD),optical disk drive and magneto-optical disk drive) for reading digitalinformation from a storage medium have been used extensively inaudiovisual appliances, personal computers and so on.

FIG. 1 is a block diagram showing a configuration for a part of aconventional optical disk drive 900. A light beam that has beenreflected from an optical disk 1 is converted by an optical head 2 intoa read signal. The read signal has its waveform shaped by a waveformequalizer 3 and then digitized by a comparator 4. The threshold value ofthe comparator 4 is normally subjected to a feedback control so that theoutput digital signals of the comparator 4 equals zero when integratedtogether.

In the optical disk drive 900, normally a phase-locked loop (PLL)circuit generates a clock signal that is synchronized with a readsignal. A clock signal of that type is termed “a read clock signal”. Asshown in FIG. 1, the PLL circuit includes a phase detector 5, a low-passfilter (LPF) 6 and a voltage controlled oscillator (VCO) 7. To generatethe read clock signal, the phase detector 5 detects a difference inphase between the output digital signal of the comparator 4 and anoutput clock signal of the VCO 7. The phase difference detected isaveraged by the LPF 6. In accordance with the output of the LPF 6, thecontrol voltage of the VCO 7 is determined. In this manner, theoscillation frequency of the VCO 7 is subjected to a feedback control sothat the phase difference output from the phase detector 5 always equalszero. Thus, the VCO 7 can output a clock signal that is synchronizedwith the read signal. By using a PLL circuit like this, even if the diskhas some degree of eccentricity, for example, a clock signal can beextracted constantly so as to be synchronized with the read signal.

The read clock signal is used to determine whether the recorded code(i.e., digital information) is one or zero. More specifically, thedigital information can be read out by determining whether or not eachdetection pulse of the comparator 4 falls within a window width definedby the read clock signal. As used herein, the “detection pulse” of thecomparator 4 refers to a portion of the output digital signal of thecomparator 4 that exceeds the predetermined threshold value.

However, the output detection pulse of the comparator 4 might deviatefrom the window width of the read clock signal due to various factorsincluding intersymbol interference occurring in the read signal, thedistortion of a recording mark, circuit noise and a control residual ofthe PLL. In that case, an error occurs. Such a time lag created betweenthe detection pulse of the comparator 4 and the read clock signal iscalled a “jitter”.

In reading digital information by the technique described above, thequality (which is represented in terms of an error rate) of the readsignal can be evaluated by using the distribution of jitter. The jitterdistribution may be supposed to form a normal distribution having a meanof zero. In that case, the error rate Pj (σ/Tw) is given by

$\begin{matrix}{{{Pj}( {\sigma/{Tw}} )} = {2\; {{erfc}( \frac{{Tw}/2}{\sigma} )}}} & (1) \\{{{erfc}(z)} = {\frac{1}{\sqrt{2\; \pi}}{\int_{z}^{\infty}{{\exp ( {- \frac{u^{2}}{2}} )}\ {u}}}}} & (2)\end{matrix}$

where σ is the standard deviation of the jitter distribution that issupposed to be a normal distribution and Tw is the window width.

FIG. 2 is a graph showing a relationship between the jitter and the biterror rate (BER). As can be seen from FIG. 2, as the standard deviationof the jitter increases, the BER also increases. The jitter of a readsignal can be actually measured with a time interval analyzer (TIA).Accordingly, even if no errors have actually occurred, the quality ofthe signal can also be evaluated by the jitter standard deviation σ perthe window width Tw. Thus, it is possible to predict the probability ofoccurrence of errors (which will be herein referred to as an “errorprobability”). For that reason, by measuring the standard deviation ofthe jitter, the performance of a given drive, a storage medium or anoptical head can be checked and tested. Also, if the parameters of anequalizer are controlled in such a manner as to decrease the standarddeviation of the jitter, then a read operation can be performed evenmore constantly.

In the technique described above, digital information is directlyobtained from the output digital signal of the comparator 4. Accordingto another known technique on the other hand, digital information mayalso be obtained by a maximum likelihood decoding method. Examples ofknown maximum likelihood decoding methods include a partial responsemaximum likelihood (PRML) method. In the PRML method, data is read orwritten from/on a storage medium having a high storage capacity with thepotential occurrence of intersymbol interference fully taken intoaccount. More specifically, a signal that has been read out from such ahigh-capacity storage medium is subjected, by a waveform equalizer, adigital filter and so on, to a partial response equalization so as tohave a predetermined frequency characteristic. Then, the PR equalizedand filtered signal is decoded into most likely (or most probable)digital data by a Viterbi decoding technique, for example. According tothe PRML method, data can be decoded at a low error rate even from aread signal with a low signal-to-noise ratio (SNR) or a read signal thatis affected by the intersymbol interference relatively seriously.

In a maximum likelihood decoding method like this, data is decoded froma read signal by selecting a most probable state transition path. Ingeneral, a quantity representing the probability of a state transitionthat leads to a state Sn (where n is a state number) at a time k isdefined by the following Equation (3):

$\begin{matrix}{L^{Sn} = {\sum\limits_{i = 0}^{k}( {y_{i} - {level}_{v}} )^{2}}} & (3)\end{matrix}$

where y_(i) is the actual value of the read signal (or digital sampledata) at a time i and level, is an expected ideal value of the readsignal.

In a maximum likelihood decoding method, a state transition path havingthe minimum probability quantity as represented by Equation (3) isselected. Unlike the above-described technique of decoding the data asone or zero by determining whether or not the detection pulse fallswithin the window width at each point in time k, a Euclidean distance of(y_(k)−level_(v))² is obtained from the data that is sampled at eachpoint in time k by reference to a read clock signal according to themaximum likelihood decoding method. Then, the data is decoded based onthe Euclidean distance. Accordingly, the decoded result obtained by themaximum likelihood decoding method is also affected by a past sampledvalue y_(k) of a read signal.

In this maximum likelihood decoding method, even when two read signalshave the same jitter standard deviation σ, errors may or may not haveoccurred in the read signals. For that reason, it is difficult toestimate the error rate of the decoded digital data, obtained by themaximum likelihood decoding method, by the jitter standard deviation σof the read signal. Accordingly, an error rate estimating method (i.e.,a signal quality evaluating method), which is more suitable to themaximum likelihood decoding method, needs to be used.

A method for evaluating the quality of a signal that has been decoded bythe maximum likelihood decoding method is disclosed in JapaneseLaid-Open Publication No. 10-21651, for example. The apparatus disclosedin Japanese Laid-Open Publication No. 10-21651 obtains a difference inlikelihood between two state transition paths, having a minimumEuclidean distance between them, and then processes this difference by astatistical method, thereby evaluating the quality of the signal.

More specifically, to obtain a difference in likelihood between twopaths that result in the same state at a time k, the sums of branchmetrics of two survived paths that were regarded as most likely for twomutually different states at the previous time k−1 are used. However,these sums of branch metrics at the time k−1 might be those of unwantedpaths. For example, a path other than the path in question (i.e., a pathhaving likelihood to be checked) may have been selected by mistakebefore the time k−1. Japanese Laid-Open Publication No. 10-21651 doesdisclose a technique of selecting two paths having the minimum Euclideandistance between them and obtaining a difference in likelihood betweenthese two paths. However, Japanese Laid-Open Publication No. 10-21651does not disclose any specific method for calculating the targetlikelihood values of these two paths with more certainty.

SUMMARY OF THE INVENTION

In order to overcome the problems described above, preferred embodimentsof the present invention provide a method and apparatus for evaluatingthe quality of a read signal by using indices that are correlated withthe error rate of digital data decoded by the maximum likelihooddecoding method.

A preferred embodiment of the present invention provides a method forevaluating the quality of a read signal that has been decoded by amaximum likelihood decoding method. In this method, a most probablestate transition path is preferably selected from a number n (where n isan integer equal to or greater than two) of state transition paths thatrepresent n probable transitions from a first state S_(k−j) (where k isan integer equal to or greater than three and j is an integer equal toor greater than two) at a time k−j into a second state S_(k) at a timek. The method preferably includes the step of detecting predeterminedcombinations of the first and second states S_(k−j) and S_(k) thatdefine the n probable state transition paths in a predetermined period jbetween the times k−j and k. The method preferably further includes thestep of evaluating the reliability of the decoded signal, obtained inthe predetermined period j, by using |Pa−Pb|. Pa and Pb are indicesindicating the respective probabilities of state transition of first andsecond state transition paths in the predetermined period j. The firstand second state transition paths are estimated to be the most probableand the second most probable, respectively, among the n probable statetransition paths that are defined by the predetermined combinationsdetected.

In one preferred embodiment of the present invention, the step ofevaluating the reliability preferably includes the steps of defining theindex Pa by differences between expected values shown by the first statetransition path and actual sample values in the predetermined period j,and defining the index Pb by differences between expected values shownby the second state transition path and the actual sample values in thepredetermined period j.

In this particular preferred embodiment, the step of evaluating thereliability preferably includes the steps of obtaining the index Pa as asum of squares of differences between the expected values l_(k−j+1), . .. , l_(k−1) and l_(k) shown by the first state transition path and theactual sample values y_(k−j+1), . . . , y_(k−1) and y_(k) in thepredetermined period j and obtaining the index Pb as a sum of squares ofdifferences between the expected values m_(k−j+1), . . . , m_(k−1) andm_(k) shown by the second state transition path and the actual samplevalues y_(k−j+1), . . . , y_(k−1) and y_(k) in the predetermined periodj.

In another preferred embodiment of the present invention, the number nis preferably two.

In still another preferred embodiment, a Euclidean distance between thefirst and second state transition paths is preferably a minimum value.

In yet another preferred embodiment, the method preferably furtherincludes the step of detecting a variation in the reliability of thedecoded signal by measuring |Pa−Pb| a number of times.

In this particular preferred embodiment, the step of detecting thevariation in the reliability may include the step of deriving a standarddeviation of a |Pa−Pb| distribution as the variation.

Alternatively, the step of detecting the variation in the reliabilitymay include the step of deriving a standard deviation and an average ofa |Pa−Pb| distribution as the variation.

As another alternative, the step of detecting the variation in thereliability may include the step of detecting a frequency of occurrenceat which |Pa−Pb| exceeds a predetermined range.

In yet another preferred embodiment, the method may further include thestep of decoding a read signal in which a recorded code has a minimumpolarity inversion interval of two and which has been subjected to a PR(C0, C1, C0) equalization.

Alternatively, the method may further include the step of decoding aread signal in which a recorded code has a minimum polarity inversioninterval of two and which has been subjected to a PR (C0, C1, C1, C0)equalization.

As another alternative, the method may further include the step ofdecoding a read signal in which a recorded code has a minimum polarityinversion interval of two and which has been subjected to a PR (C0, C1,C2, C1, C0) equalization.

In yet another preferred embodiment, the step of evaluating thereliability may include the step of obtaining |Pa−Pb| withoutcalculating squares of the actual sample values.

Another preferred embodiment of the present invention provides anapparatus for reading information. The apparatus preferably includesgain controller, first waveform equalizer, read clock signal generator,A/D converter, maximum likelihood decoder and differential metriccalculator. The gain controller preferably adjusts an amplitude value ofa read signal. The first waveform equalizer preferably shapes thewaveform of the read signal so that the read signal has a predeterminedequalization characteristic. The read clock signal generator preferablygenerates a read clock signal that is synchronized with the read signal.The A/D converter preferably generates and outputs sampled data bysampling the read signal in response to the read clock signal. Themaximum likelihood decoder preferably decodes the sampled data into mostlikely digital information. The differential metric calculatorpreferably obtains |Pa−Pb|. Pa and Pb are indices indicating respectiveprobabilities of state transition of first and second state transitionpaths in a predetermined period. The first and second state transitionpaths are estimated by the maximum likelihood decoder to be the mostprobable and the second most probable, respectively.

In one preferred embodiment of the present invention, the apparatuspreferably further includes a second waveform equalizer for shaping thewaveform of the read signal differently from the first waveformequalizer so that the read signal has another predetermined equalizationcharacteristic. In that case, the read clock signal is preferablygenerated from the read signal that has had its waveform shaped by thesecond waveform equalizer.

Other features, elements, processes, steps, characteristics andadvantages of the present invention will become more apparent from thefollowing detailed description of preferred embodiments of the presentinvention with reference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a configuration for aconventional optical disk drive.

FIG. 2 is a graph showing a relationship between the jitter and the biterror rate (BER).

FIG. 3 is a state transition diagram that is defined by the constraints,including a minimum polarity inversion interval of two and the use of aPR (1, 2, 2, 1) equalization technique, according to a preferredembodiment of the present invention.

FIG. 4 is a trellis diagram that is defined by the constraints,including the minimum polarity inversion interval of two and the use ofthe PR (1, 2, 2, 1) equalization technique, in the preferred embodimentof the present invention.

FIG. 5 is a diagram showing two possible state transition paths betweenstates S0 _(k) and S0 _(k−5) that are extracted from the trellis diagramshown in FIG. 4.

FIGS. 6A and 6B are graphs schematically showing the distributions ofthe reliability Pa−Pb of the decoded result.

FIG. 7 is a block diagram illustrating a configuration for an opticaldisk drive %; as an exemplary apparatus for evaluating the quality of aread signal according to a third specific preferred embodiment of thepresent invention.

FIG. 8 is a block diagram illustrating detailed configurations of theViterbi circuit and differential metric analyzer of the optical diskdrive shown in FIG. 7.

FIG. 9 is a diagram illustrating a detailed configuration of the pathmemory of the optical disk drive shown in FIG. 7.

FIG. 10 is a block diagram illustrating a configuration for anotheroptical disk drive according to the third preferred embodiment.

FIG. 11 is a block diagram illustrating a configuration for stillanother optical disk drive according to the third preferred embodiment.

FIG. 12 is a block diagram illustrating a configuration for yet anotheroptical disk drive according to the third preferred embodiment.

FIG. 13 is a block diagram illustrating a configuration for an opticaldisk drive according to a fourth specific preferred embodiment of thepresent invention.

FIG. 14 is a block diagram illustrating a configuration for anotheroptical disk drive according to the fourth preferred embodiment.

FIG. 15 is a block diagram illustrating a configuration for stillanother optical disk drive according to the fourth preferred embodiment.

FIG. 16 is a graph showing a relationship between the PRML error indexMLSA and the bit error rate (BER).

FIG. 17 is a state transition diagram that is defined by theconstraints, including a minimum polarity inversion interval of two andthe use of a PR (C0, C1, C0) equalization technique, according toanother preferred embodiment of the present invention.

FIG. 18 is a trellis diagram that is defined by the constraints,including the minimum polarity inversion interval of two and the use ofthe PR (C0, C1, C0) equalization technique, in the preferred embodimentof the present invention.

FIG. 19 is a state transition diagram that is defined by theconstraints, including a minimum polarity inversion interval of two andthe use of a PR (C0, C1, C2, C1, C0) equalization technique, accordingto another preferred embodiment of the present invention.

FIG. 20 is a trellis diagram that is defined by the constraints,including the minimum polarity inversion interval of two and the use ofthe PR (C0, C1, C2, C1, C0) equalization technique, in the preferredembodiment of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Embodiment 1

Hereinafter, a method for evaluating the quality of a read signal and anapparatus for reading information according to preferred embodiments ofthe present invention will be described with reference to theaccompanying drawings.

First, a read signal quality evaluating method according to a preferredembodiment of the present invention will be described. In the preferredembodiments to be described below, a code having a minimum polarityinversion interval of two, e.g., a code defined by a (1, 7) RLLmodulation method, is used as the recorded code. That is to say, anyrecorded code always has two or more consecutive zeros or ones. Also, asignal is supposed to be decoded by a PRML method in which the frequencycharacteristics of read and write systems substantially correspond to aPR (1, 2, 2, 1) equalization characteristic as a whole. Hereinafter, aspecific decoding procedure will be described.

Suppose recorded codes (each being made up of zeros or ones) are denotedby:

Current recorded code: b_(k);

Recording code at the previous time: b_(k−1);

Recording code at the second last time: b_(k−2); and

Recording code at the third last time: b_(k−3)

An ideal value Level_(v) of a read signal that has been subjected to thePR (1, 2, 2, 1) equalization is given by:

Level_(v) =b _(k−3)+2b _(k−2)+2b _(k−1) +b _(k)  (4)

where k is an integer, representing the time and v is an integer of 0 to6. In the PR (1, 2, 2, 1) equalization, there are seven ideal samplevalues (or expected values) Level_(v) (where 0≦v≦6) depending on thecombination of the recorded codes.

Next, the state transitions of the recorded codes will be described. Astate at the time k is represented by S (b_(k−2), b_(k−1), b_(k)) and astate at the previous time k−1 is represented by S (b_(k−3), b_(k−2),b_(k−1)). The following Table 1 is a table of state transitions that iscompiled by obtaining possible combinations of states at the times k−1and k. As described above, a modulation technique that defines theminimum inversion interval at two (i.e., at least two zeros or onesappear consecutively) is adopted in this preferred embodiment.Accordingly, the possible state transitions that a recorded code canmake are limited to the following ten:

TABLE 1 State State S (b_(k−3), b_(k−2), b_(k−1)) S (b_(k−2), b_(k−1),b_(k)) at time k − 1 at time k b_(k)/Level_(v) S (0, 0, 0) S (0, 0, 0)0/0 S (0, 0, 0) S (0, 0, 1) 1/1 S (0, 0, 1) S (0, 1, 1) 1/3 S (0, 1, 1)S (1, 1, 0) 0/4 S (0, 1, 1) S (1, 1, 1) 1/5 S (1, 0, 0) S (0, 0, 0) 0/1S (1, 0, 0) S (0, 0, 1) 1/2 S (1, 1, 0) S (1, 0, 0) 0/3 S (1, 1, 1) S(1, 1, 0) 0/5 S (1, 1, 1) S (1, 1, 1) 1/6

In the following description, the states S (0, 0, 0)_(k), S (0, 0,1)_(k), S (0, 1, 1)_(k), S (1, 1, 1)_(k), S (1, 1, 0)_(k), S (1, 0,0)_(k) and so on at the time k will be identified by S0 _(k), S1 _(k),S2 _(k), S3 _(k), S4 _(k), S5 _(k) and so on, respectively, for the sakeof simplicity. The state transitions that may occur in the periodbetween the time k−1 and the time k (i.e., a period of timecorresponding to one cycle T of a read clock signal) are represented bythe state transition diagram shown in FIG. 3. When the state transitiondiagram shown in FIG. 3 is expanded with respect to the time axis, thetrellis diagram shown in FIG. 4 is obtained.

Look at the state S0 _(k) at the time k and the state S0 _(k−5) at atime k−5 shown in FIG. 5. In FIG. 5, two possible paths of statetransitions that can occur between the states S0 _(k) and S0 _(k−5) areindicated by the bold arrows. One A of the two possible state transitionpaths goes through the states S0 _(k−5), S0 _(k−4), S0 _(k−3), S0_(k−2), S0 _(k−1) and S0 _(k), while the other possible state transitionpath B goes through the states S0 _(k−5). S1 _(k−4), S2 _(k−3), S4_(k−2), S5 _(k−1) and S0 _(k). In FIGS. 4 and 5, (recordedcode/Level_(v)) is shown for each state transition. In this case,Level_(v) is supposed to be any value between −3 and 3. That is to say,the Level_(v) values of −3, −2, −1, 0, 1, 2 and 3 correspond to Level₀,Level₁, Level₂, Level₃, Level₄, Level₅, and Level₆, respectively.

In this manner, if the states at the times k−5 and k are S0 _(k−5) andS0 _(k), respectively, it is estimated that the state transitions shouldhave occurred along one of the two paths A and B. That is to say, if thedecoded result obtained, i.e., the data that has been decoded in aperiod between the times k−7 and k, is (C_(k−7), C_(k−6), C_(k−5),C_(k−4), C_(k−3), C_(k−2), C_(k−1), C_(k))=(0, 0, 0, x, x, 0, 0, 0)(where x is either zero or one), then the state transition path A or Bis estimated to be the most probable one.

If the states S0 _(k) and S0 _(k−5) are detected at the times k and k−5,respectively (i.e., if the decoded result obtained is (0, 0, 0, x, x, 0,0, 0)), then it is necessary to determine which is more probable, thepath A or the path B. This decision can be made by comparing the sum oferrors (or differences) between ideal sample values (i.e., expectedvalues) shown by the path A and actual sample values with that of errorsbetween ideal sample values (i.e., expected values) shown by the path Band the actual sample values. More specifically, for each of these twopaths A and B, errors between expected values Level_(v) at the timesk−4, k−3, k−2, k−1 and k and the actual values y_(k−4), y_(k−3),y_(k−2), y_(k−1) and y_(k) of the read signal are obtained. The squaresof these errors are summed up, thereby obtaining a sum of squared errorsfor each of the paths A and B. By comparing these sums of squared errorsof the paths A and B with each other, it is possible to determine whichof the two paths A and B is the more probable one.

In this case, the sum of squared errors between the expected valuesl_(k−4), l_(k−3), l_(k−2), l_(k−1) and l_(k) (i.e., 0, 0, 0, 0, 0) shownby the path A and the values y_(k−4), y_(k−3), y_(k−2), y_(k−1) andy_(k) of the read signal at the times k−4, k−3, k−2, k−1 and k,respectively, is identified by Pa. On the other hand, the sum of squarederrors between the expected values m_(k−4), m_(k−3), m_(k−2), m_(k−1)and m_(k) (i.e., 1, 3, 4, 3, 1) shown by the path B and the valuesy_(k−4), y_(k−3), y_(k−2), y_(k−1) and y_(k) of the read signal at thetimes k−4, k−3, k−2, k−1 and k, respectively, is identified by Pb. Thesesums of squared errors Pa and Pb are respectively given by the followingEquations (5) and (6):

Pa=(y _(k−4)−0)²+(y _(k−3)−0)²+(y _(k−2)−0)²+(y _(k−1)−0)²+(y_(k)−0)²  (5)

Pb=(y _(k−4)−1)²+(y _(k−3)−3)²+(y _(k−2)−4)²+(y _(k−1)−3)²+(y_(k)−1)²  (6)

The sum of squared errors Pa obtained in this manner is an indexindicating the probability of state transitions of the path A in thepredetermined period between the times k−5 and k. That is to say, thesmaller the Pa value, the more probable the path A will be. On the otherhand, the sum of squared errors Pb obtained in this manner is an indexindicating the probability of state transitions of the path B in thepredetermined period between the times k−5 and k. That is to say, thesmaller the Pb value, the more probable the path B will be. Also, if thePa or Pb value is zero, then the path A or B is estimated to be the mostprobable one.

Next, it will be described what the difference Pa−Pb between the Pa andPb values means. A maximum likelihood decoder does not hesitate tochoose the path A if Pa<<Pb or the path B if Pa>>Pb. However, if Pa=Pb,then either the path A or the path B may be chosen and the decodedresult may or may not be true. Thus, the Pa−Pb value may be used as ameasure of the reliability of the decoded result. That is to say, thegreater the absolute value of Pa−Pb, the higher the reliability of thedecoded result should be. On the other hand, the closer to zero theabsolute value of Pa−Pb, the lower the reliability of the decoded resultshould be.

This Pa−Pb index indicating the reliability of the decoded result isused to evaluate the quality of the read signal. For that purpose, byobtaining the Pa−Pb values for a predetermined amount of time or apredetermined number of times based on the decoded results, a Pa−Pbdistribution is obtained. FIGS. 6A and 6B schematically illustrate thePa−Pb distributions. Specifically, FIG. 6A shows a Pa−Pb distributionwhere noise is superposed on the read signal. As shown in FIG. 6A, thisdistribution has two peaks. One of the two peaks corresponds to afrequency of occurrence that reaches a local maximum value when Pa=0.The other peak corresponds to a frequency of occurrence that reaches alocal maximum value when Pb=0. The Pa−Pb value corresponding to the zeroPa value will be herein identified by −Pstd and the Pa−Pb valuecorresponding to the zero Pb value will be herein identified by Pstd.When Pstd is subtracted from the absolute value of Pa−Pb (i.e., when|Pa−Pb|−Pstd is calculated), the distribution shown in FIG. 6B isobtained.

By supposing this distribution to be a normal distribution, the standarddeviation σ and the average Pave of the distribution are obtained. Thestandard deviation σ and average Pave of this distribution may be usedto estimate a bit error rate. For example, if the estimated |Pa−Pb|distribution is curved gently and defined by a function that may have avalue of zero or less (i.e., unless the frequency of occurrence of|Pa−Pb|=0 is zero), decoding errors may be regarded as occurring at afrequency of occurrence that corresponds to the probability at which thefunction becomes zero or less. In that case, the error probability P (σ,Pave) may be defined by the following Equation (7) using the standarddeviation σ and the average Pave:

P(σ, Pave)=erfc(Pstd+Pave/σ)  (7)

In this manner, the error rate of the digital decoded result obtained bya maximum likelihood decoding method can be estimated by using theaverage Pave and the standard deviation σ that have been derived fromthe distribution of Pa−Pb. In other words, the average Pave and thestandard deviation σ may be used as indices to the quality of the readsignal. In the example described above, the |Pa−Pb| distribution issupposed to be a normal distribution. But if it is difficult to regardthe |Pa−Pb| distribution as a normal distribution, then it is possibleto count how many times the |Pa−Pb| values are equal to or smaller thana predetermined reference value instead of deriving the average Pave andthe standard deviation σ as described above. The count obtained in thismanner may be used as an index indicating the degree of variance of the|Pa−Pb| values.

According to the preferred embodiment described above, if a statetransition has occurred from a first predetermined state (e.g., S0_(k−5)) into a second predetermined state (e.g., S0 _(k)) during apredetermined period, the absolute value of the difference |Pa−Pb|between the probabilities of two possible paths in the predeterminedperiod is calculated, thereby evaluating the reliability of the decodedresult. Furthermore, by measuring the |Pa−Pb| values a number of times,a variance (or distribution) representing the degree of reliability|Pa−Pb| of the decoded result can be obtained. In this manner, thequality of the read signal can be evaluated (i.e., the bit error rate ofthe read signal can be estimated).

It should be noted that in evaluating the signal quality by such amethod, a combination of states, between which a state transition shouldhave occurred along one of the two paths having the highest errorprobabilities (i.e., two paths having a minimum Euclidean distancebetween them), is preferably selected, and the signal quality may beevaluated by reference to the absolute value |Pa−Pb| of the differencebetween the probabilities of these two paths. Hereinafter, this pointwill be described in detail.

In decoding a read signal in accordance with the above-described statetransition rule that requires the use of a minimum polarity inversioninterval of two in combination with the PR (1, 2, 2, 1) equalization,not just the S0 _(k−5)→S0 _(k) state transition but also fifteen otherstate transitions may occur along two paths in the period between thetimes k−5 and k. The following Table 2 lists those sixteen statetransitions (i.e., 16 combinations of states at the times k−5 and k)with their respective possible Pa−Pb (or Pstd) values:

TABLE 2 Reliability Pa − Pb State of decoded result transition If Pa = 0If Pb = 0 S0_(k−5)

 S0_(k) −36 +36 S0_(k−5) → S1_(k) −36 +36 S0_(k−4) → S4_(k) −10 +10S0_(k−4) → S3_(k) −10 +10 S2_(k−4) → S0_(k) −10 +10 S2_(k−4) → S1_(k)−10 +10 S2_(k−5) → S4_(k) −36 +36 S2_(k−5) → S3_(k) −36 +36 S5_(k−5) →S0_(k) −36 +36 S5_(k−5) → S1_(k) −36 +36 S5_(k−4) → S4_(k) −10 +10S5_(k−4) → S3_(k) −10 +10 S3_(k−4) → S0_(k) −10 +10 S3_(k−4) → S1_(k)−10 +10 S3_(k−5) → S4_(k) −36 +36 S3_(k−5) → S3_(k) −36 +36

The reliabilities Pa−Pb of the sixteen decoded results are given by thefollowing Equations (8.1) through (8.16):

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(0,0,0,x,x,0,0,0), then Pa−Pb=(A _(k−4) −B _(k−4))+(A _(k−3) −D_(k−3))+(A _(k−2) −E _(k−2))+(A _(k−1) −D _(k−1))+(A _(k) −B_(k));  (8.1)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(0,0,0,x,x,0,0,0), then Pa−Pb=(A _(k−4) −B _(k−4))+(A _(k−3) −D_(k−3))+(A _(k−2) −E _(k−2))+(A _(k−1) −D _(k−1))+(B _(k) −C_(k));  (8.2)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(0,0,0,x,1,1,0), then Pa−Pb=(A _(k−3) −B _(k−3))+(B _(k−2) −D_(k−2))+(D _(k−1) −F _(k−1))+(E _(k) −F _(k));  (8.3)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(0,0,0,x,1,1,1), then Pa−Pb=(A _(k−3) −B _(k−3))+(B _(k−2) −D_(k−2))+(D _(k−1) −F _(k−1))+(F _(k) −G _(k));  (8.4)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(0,1,1,x,0,0,0), then Pa−Pb=(E _(k−3) −F _(k−3))+(D _(k−2) −F_(k−2))+(B _(k−1) −D _(k−1))+(A _(k) −B _(k));  (8.5)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(0,1,1,x,0,0,1), then Pa−Pb=(E _(k−3) −F _(k−3))+(D _(k−2) −F_(k−2))+(B _(k−1) −D _(k−1))+(B _(k) −C _(k));  (8.6)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c_(k−1),c_(k))=(0,1,1,x,x,1,1,0), then Pa−Pb=(E _(k−4) −F _(k−4))+(D_(k−3) −G _(k−3))+(C _(k−2) −G _(k−2))+(D _(k−1) −G _(k−1))+(E _(k) −F_(k));  (8.7)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c_(k−1),c_(k))=(0,1,1,x,x,1,1,1), then Pa−Pb=(E _(k−4) −F _(k−4))+(D_(k−3) −G _(k−3))+(C _(k−2) −G _(k−2))+(D _(k−1) −G _(k−1))+(F _(k) −G_(k));  (8.8)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c_(k−1),c_(k))=(1,0,0,x,x,0,0,0), then Pa−Pb=(B _(k−4) −C _(k−4))+(A_(k−3) −D _(k−3))+(A _(k−2) −E _(k−2))+(A _(k−1) −D _(k−1))+(A _(k) −B_(k));  (8.9)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c_(k−1),c_(k))=(1,0,0,x,x,0,0,1), then Pa−Pb=(B _(k−4) −C _(k−4))+(A_(k−3) −D _(k−3))+(A _(k−2) −E _(k−2))+(A _(k−1) −D _(k−1))+(B _(k) −C_(k));  (8.10)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(1,0,0,x,1,1,0), then Pa−Pb=(B _(k−3) −C _(k−3))+(B _(k−2) −D_(k−2))+(D _(k−1) −F _(k−1))+(E _(k) −F _(k));  (8.11)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(1,0,0,x,1,1,1), then Pa−Pb=(B _(k−3) −C _(k−3))+(B _(k−2) −D_(k−2))+(D _(k−1) −F _(k−1))+(F _(k) −G _(k));  (8.12)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(1,1,1,x,0,0,0), then Pa−Pb=(F _(k−3) −G _(k−3))+(D _(k−2) −F_(k−2))+(B _(k−1) −D _(k−1))+(A _(k) −B _(k));  (8.13)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(1,1,1,x,0,0,0), then Pa−Pb=(F _(k−3) −G _(k−3))+(D _(k−2) −F_(k−2))+(B _(k−1) −D _(k−1))+(B _(k) −C _(k));  (8.14)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(1,1,1,x,x,1,1,0), then Pa−Pb=(F _(k−4) −G _(k−4))+(D _(k−3) −G_(k−3))+(C _(k−2) −G _(k−2))+(D _(k−1) −G _(k−1))+(E _(k) −F _(k));and  (8.15)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(1,1,1,x,x,1,1,1), then Pa−Pb=(F _(k−4) −G _(k−4))+(D _(k−3) −G_(k−3))+(C _(k−2) −G _(k−2))+(D _(k−1) −G _(k−1))+(F _(k) −G_(k)).  (8.16)

where A_(k)=(y_(k)−0)², B_(k)=(y_(k)−1)², C_(k)=(y_(k)−2)²,D_(k)=(y_(k)−3)², E_(k)=(y_(k)−4)², F_(k)=(y_(k)−5)² andG_(k)=(y_(k)−6)².

These Equations (8.1) through (8.16) may be classified by the Pstd valueinto the following two group of Equations (9.1) through (9.8) (wherePstd=10) and (10.1) through (10.8) (where Pstd=36):

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(0,0,0,x,1,1,0), then Pa−Pb=(A _(k−3) −B _(k−3))+(B _(k−2) −D_(k−2))+(D _(k−1) −F _(k−1))+(E _(k) −F _(k));  (9.1)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(0,0,0,x,1,1,1), then Pa−Pb=(A _(k−3) −B _(k−3))+(B _(k−2) −D_(k−2))+(D _(k−1) −F _(k−1))+(F _(k) −G _(k));  (9.2)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(0,1,1,x,0,0,0), then Pa−Pb=(E _(k−3) −F _(k−3))+(D _(k−2) −F_(k−2))+(B _(k−1) −D _(k−1))+(A _(k) −B _(k));  (9.3)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(0,1,1,x,0,0,1), then Pa−Pb=(E _(k−3) −F _(k−3))+(D _(k−2) −F_(k−2))+(B _(k−1) −D _(k−1))+(B _(k) −C _(k));  (9.4)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(1,0,0,x,1,1,0), then Pa−Pb=(B _(k−3) −C _(k−3))+(B _(k−2) −D_(k−2))+(D _(k−1) −F _(k−1))+(E _(k) −F _(k));  (9.5)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(1,0,0,x,1,1,1), then Pa−Pb=(B _(k−3) −C _(k−3))+(B _(k−2) −D_(k−2))+(D _(k−1) −F _(k−1))+(F _(k) −G _(k));  (9.6)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(1,1,1,x,0,0,0), then Pa−Pb=(F _(k−3) −G _(k−3))+(D _(k−2) −F_(k−2))+(B _(k−1) −D _(k−1))+(A _(k) −B _(k)); and  (9.7)

If (c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c_(k))=(1,1,1,x,0,0,1), then Pa−Pb=(F _(k−3) −G _(k−3))+(D _(k−2) −F_(k−2))+(B _(k−1) −D _(k−1))+(B _(k) −C _(k));  (9.8)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(0,0,0,x,x,0,0,0), then Pa−Pb=(A _(k−4) −B _(k−4))+(A _(k−3) −D_(k−3))+(A _(k−2) −E _(k−2))+(A _(k−1) −D _(k−1))+(A _(k) −B_(k));  (10.1)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(0,0,0,x,x,0,0,1), then Pa−Pb=(A _(k−4) −B _(k−4))+(A _(k−3) −D_(k−3))+(A _(k−2) −E _(k−2))+(A _(k−1) −D _(k−1))+(B _(k) −C_(k));  (10.2)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(0,1,1,x,x,1,1,0), then Pa−Pb=(E _(k−4) −F _(k−4))+(D _(k−3) −G_(k−3))+(C _(k−2) −G _(k−2))+(D _(k−1) −G _(k−1))+(E _(k) −F_(k));  (10.3)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(0,1,1,x,x,1,1,1), then Pa−Pb=(E _(k−4) −F _(k−4))+(D _(k−3) −G_(k−3))+(C _(k−2) −G _(k−2))+(D _(k−1) −G _(k−1))+(F _(k) −G_(k));  (10.4)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(1,0,0,x,x,0,0,0), then Pa−Pb=(B _(k−4) −C _(k−4))+(A _(k−3) −D_(k−3))+(A _(k−2) −E _(k−2))+(A _(k−1) −D _(k−1))+(A _(k) −B_(k));  (10.5)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(1,0,0,x,x,0,0,1), then Pa−Pb=(B _(k−4) −C _(k−4))+(A _(k−3) −D_(k−3))+(A _(k−2) −E _(k−2))+(A _(k−1) −D _(k−1))+(B _(k) −C_(k));  (10.6)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(1,1,1,x,x,1,1,0), then Pa−Pb=(F _(k−4) −G _(k−4))+(D _(k−3) −G_(k−3))+(C _(k−2) −G _(k−2))+(D _(k−1) −G _(k−1))+(E _(k) −F _(k));and  (10.7)

If (c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1),c _(k))=(1,1,1,x,x,1,1,1), then Pa−Pb=(F _(k−4) −G _(k−4))+(D _(k−3) −G_(k−3))+(C _(k−2) −G _(k−2))+(D _(k−1) −G _(k−1))+(F _(k) −G_(k))  (10.8)

Hereinafter, it will be described how to obtain error rate indices toeach of these possible state transitions. As for the eight statetransitions having a Pstd value of 10, Pa−Pb values satisfying Equations(9.1) through (9.8) are obtained from the most likely decoded resultsc_(k) and the standard deviation σ₁₀ and average Pave₁₀ are obtainedfrom their distribution. As for the other eight state transitions havinga Pstd value of 36 on the other hand, Pa−Pb values satisfying Equations(10.1) through (10.8) are obtained from the most likely decoded resultsc_(k) and the standard deviation σ₃₆ and average Pave₃₆ are obtainedfrom their distribution. Supposing these distributions are both normaldistributions, the error probabilities P₁₀ and P₃₆ are respectivelygiven by the following Equations (11) and (12):

$\begin{matrix}{{P_{10}( {\sigma_{10},{Pave}_{10}} )} = {{erfc}( \frac{10 + {Pave}_{10}}{\sigma_{10}} )}} & (11) \\{{P_{36}( {\sigma_{36},{Pave}_{36}} )} = {{erfc}( \frac{36 + {Pave}_{36}}{\sigma_{36}} )}} & (12)\end{matrix}$

That is to say, the error rate can be estimated for each pattern of themost likely decoded results. Thus, the standard deviation σ₁₀ andaverage Pave₁₀ or the standard deviation σ₃₆ and average Pave₃₆ may beused as indices to the quality of the read signal.

If the state transition pattern detection range is expanded by one timeperiod (i.e., when combination patterns of state transitions, each ofwhich should have occurred along one of two paths, are detected in theperiod between the time k−6 and the time k), the eight patterns shown inthe following Table 3 may be further detected:

TABLE 3 Reliability Pa − Pb State of decoded result transition If Pa = 0If Pb = 0 S0_(k−6) → S0_(k) −12 +12 S0_(k−6) → S1_(k) −12 +12 S2_(k−6) →S3_(k) −12 +12 S2_(k−6) → S4_(k) −12 +12 S5_(k−6) → S0_(k) −12 +12S5_(k−6) → S1_(k) −12 +12 S3_(k−6) → S3_(k) −12 +12 S3_(k−6) → S4_(k)−12 +12

Just like the Equations (11) and (12), the error probability P₁₂ of eachof the eight patterns shown in Table 3 is given by the followingEquation (13):

$\begin{matrix}{{P_{12}( {\sigma_{12},{Pave}_{12}} )} = {{erfc}( \frac{12 + {Pave}_{12}}{\sigma_{12}} )}} & (13)\end{matrix}$

The point is that the reliability |Pa−Pb| may be used effectively as anindex to the quality of the read signal by detecting only statetransition patterns having relatively high error probabilities (or errorrates). That is to say, an index correlated with the error rate can beobtained without detecting all state transition patterns.

As used herein, the “state transition patterns having relatively higherror probabilities” refer to state transition patterns of which themaximum value of the reliability values Pa−Pb| is relatively small(i.e., patterns having the smallest Euclidean distance, or the absolutedistance between the paths A and B). In this example, the “statetransition patterns having relatively high error probabilities” are theeight patterns shown in Table 2 in which Pa−Pb=±10 when Pa=0 or Pb=0.

If white noise prevails in the noise included in the read signal, it isexpected that an inequality P₁₀>P₁₂>>P₃₆ is satisfied. Among these threeerror probabilities, only P₁₀ means a shift error of one bit, while theother two P₁₂ and P₃₆ mean a shift error of two or more bits. Generallyspeaking, almost all error patterns are found to be one-bit shift errorsafter PRML processing has been performed. Accordingly, the error rate ofthe read signal may be appropriately estimated by Equation (11) thatdefines the error probability P₁₀. In this manner, the quality of theread signal may be evaluated by detecting patterns representingpredetermined state transitions in a predetermined period and by using,as indices, the standard deviation σ₁₀, and average Pave₁₀ of the|Pa−Pb|−Pstd distribution of the state transition patterns detected.

As described above, the error rate may be estimated by using thestandard deviation σ₁₀. Alternatively, a maximum likelihood sequenceamplitude (MLSA), which is an error index for use in PRML processing(which will be herein simply referred to as an “MLSA index”), may alsobe used as an index to the signal quality (or error rate). The MLSAindex is defined by the following Equation (14):

$\begin{matrix}{M = {\frac{\sigma_{10}}{2 \cdot d_{\min}^{2}}\lbrack\%\rbrack}} & (14)\end{matrix}$

where d² _(min) is the square of the minimum Euclidean distance betweentwo possible paths. In the combination of modulation code and PRMLmethod as adopted in this preferred embodiment, d² _(min)=10. This MLSAindex is obtained by Equation (14) on the supposition that the averagePave₁₀ used in Equation (11) is zero (i.e., while leaving the averagePave₁₀ out of consideration). This is because the average Pave₁₀ istypically approximately zero and normally does not constitute a majorfactor of decreasing the correlation between the index and the errorrate.

FIG. 16 shows a relationship between the MLSA index as defined byEquation (14) and a bit error rate BER as derived by Equation (11). Itcan be seen that just like the jitter-error rate relationship shown inFIG. 2, as the MLSA index increases, the error rate increases. That isto say, it can be seen that the error rate to be obtained after the PRMLprocessing may be estimated by using the MLSA index.

In the specific preferred embodiment described above, a PR (1, 2, 2, 1)equalization technique is used as an exemplary PR (C0, C1, C1, C0)equalization technique (where C0 and C1 are arbitrary positiveintegers). However, even if any other PR (C0, C1, C1, C0) equalizationtechnique (where C0 and C1 are arbitrary positive integers) is adopted,an index correlated with the error rate can also be obtained through asimilar procedure.

Hereinafter, another specific preferred embodiment of the presentinvention will be described. In the following specific preferredembodiment, a recorded code having a minimum polarity inversion intervalof two is used as in the preferred embodiment described above. However,unlike the preferred embodiment described above, a PR (C0, C1, C0)(where C0 and C1 are arbitrary positive integers) equalization technique(e.g., PR (1, 2, 1) equalization) is applied to the following preferredembodiment.

Suppose recorded codes (each being made up of zeros or ones) are denotedby:

Current recorded code: b_(k);

Recording code at the previous time: b_(k−1); and

Recording code at the second last time: b_(k−2)

An ideal value Level_(v) of a read signal that has been subjected to thePR (C0, C1, C0) equalization is given by the following Equation (15):

Level_(v) =C0×b _(k−2) +C1×b _(k−1) +C0×b _(k)  (15)

where k is an integer representing a time and v is an integer of 0 to 3.Supposing a state at a time k is identified by S (b_(k−1), b_(k)), atable of state transitions such as the following Table 4 is obtained:

TABLE 4 State S (b_(k−2), b_(k−1)) State S (b_(k−1), b_(k)) at time k −1 at time k b_(k)/LEVEL_(v) S (0, 0) S (0, 0) 0/0 S (0, 0) S (0, 1) 1/C0S (0, 1) S (1, 1) 1/C0 + C1 S (1, 1) S (1, 0) 0/C1 + C0 S (1, 1) S(1, 1) 1/C0 + C1 + C0 S (1, 0) S (0, 0) 0/C0

In the following description, the states S (0, 0)_(k), S (0, 1)_(k), S(1, 1)_(k), S (1, 0)_(k) and so on at the time k will be identified byS0 _(k), S1 _(k), S2 _(k), S3 _(k) and so on, respectively, for the sakeof simplicity. The state transitions that may occur in the periodbetween the time k−1 and the time k (i.e., a period of timecorresponding to one cycle T of a read clock signal) are represented bythe state transition diagram shown in FIG. 17. When the state transitiondiagram shown in FIG. 17 is expanded with respect to the time axis, thetrellis diagram shown in FIG. 18 is obtained.

In this preferred embodiment, each recorded code has a minimum polarityinversion interval of two and the PR (C0, C1, C0) equalization techniqueis used. Under these conditions, there are six possible state transitionpatterns (i.e., possible combinations of states) as for statetransitions occurring from a predetermined state at a time into anotherpredetermined state at a different time along two paths (i.e., paths Aand B) as shown in the following Table 5:

TABLE 5 Recording code Recording code State (b_(k−i), . . . , b_(k)) of(b_(k−i), . . . , b_(k)) of transition path A path B S0_(k−3) → S2_(k)(0, 0, 0, 1, 1) (0, 0, 1, 1, 1) S2_(k−3) → S0_(k) (1, 1, 0, 0, 0) (1, 1,1, 0, 0) S0_(k−4) → S0_(k) (0, 0, 0, 0, 0, 0) (0, 0, 1, 1, 0, 0)S2_(k−4) → S2_(k) (1, 1, 0, 0, 1, 1) (1, 1, 1, 1, 1, 1) S0_(k−5) →S0_(k) (0, 0, 0, 1, 1, 0, 0) (0, 0, 1, 1, 0, 0, 0) S2_(k−5) → S2_(k) (1,1, 0, 0, 0, 1, 1) (1, 1, 1, 0, 0, 1, 1)

In this case, it is determined which of the two paths A and B has thehigher probability. This decision can be made by comparing the sum oferrors between ideal sample values (i.e., expected values) shown by thepath A and actual sample values with the sum of errors betweenassociated ideal sample values (i.e., expected values) shown by the pathB and the actual sample values.

For example, suppose the state transition S0 _(k−3)→S2 _(k) should beestimated. As for this state transition, no matter whether the path A(S0 _(k−3), S0 _(k−2), S1 _(k−1), S2 _(k)) or the path B (S0 _(k−3), S1_(k−2), S2 _(k−1), S2 _(k)) has been taken, the state at the time k−3 isS0 _(k−3) and the state at the time k is S2 _(k). In this case, it is byusing the sum of squared errors between the expected values and theactual values y_(k−2), y_(k−1), and y_(k) of the read signal in theperiod between the times k−2 and k that it is determined which of thetwo paths A and B has the higher probability. As in the preferredembodiment described above,

the sum of squared errors between the expected values shown by the pathA and the actual values y_(k−2), y_(k−1) and y_(k) of the read signal inthe period between the times k−2 and k is identified by Pa. On the otherhand, the sum of squared errors between the expected values shown by thepath B and the actual values y_(k−2), y_(k−1), and y_(k) of the readsignal in the period between the times k−2 and k is identified by Pb.These sums of squared errors Pa and Pb (i.e., the error probabilities)are respectively given by the following Equations (16) and (17):

Pa=(y _(k−2)−0)²+(y _(k−1) C0)²+(y _(k)−(C0+C1))²  (16)

Pb=(y _(k−2) −C0)²+(y _(k−1)−(C0+C1))²+(y _(k)−(2×C0+C1))²  (17)

In this case, if Pa<<Pb, then the path A is estimated to be the moreprobable one. On the other hand, if Pa>>Pb, then the path B is estimatedto be the more probable one. That is to say, even when a recorded codehaving a minimum polarity inversion interval of two is combined with thePR (C0, C1, C0) equalization technique, the reliability of the decodedresult can also be evaluated by |Pa−Pb|. Also, the quality of the readsignal can be evaluated (or the error rate can be estimated) based onthe |Pa−Pb| distribution.

Furthermore, suppose white noise has been superposed on the transmissionline. In that case, a state transition having the highest errorprobability should have a minimum Euclidean distance between the paths Aand B. The two state transition patterns shown in the following Table 6should have the minimum Euclidean distance between their two paths:

TABLE 6 Recording code Recording code (b_(k−4), b_(k−3), (b_(k−4),b_(k−3), State b_(k−2), b_(k−1), b_(k)) b_(k−2), b_(k−1), b_(k))transition of path A of path B S0_(k−3) → S2_(k) (0, 0, 0, 1, 1) (0, 0,1, 1, 1) S2_(k−3) → S0_(k) (1, 1, 0, 0, 0) (1, 1, 1, 0, 0)

The reliabilities Pa−Pb of the two state transition patterns shown inTable 6 are given by the following Equations (18.1) and (18.2):

If (c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c _(k))=(0,0,x,1,1), thenPa−Pb=(AA _(k−2) −BB _(k−2))+(BB _(k−1) −CC _(k−1))+(CC _(k) −DD _(k));and  (18.1)

If (c _(k−4) ,c _(k−3) ,c _(k−2) ,c _(k−1) ,c _(k))=(1,1,x,0,0), thenPa−Pb=(CC _(k−2) −DD _(k−2))+(BB _(k−1) −CC _(k−1))+(AA _(k) −BB_(k))  (18.1)

where c_(k) is the decoded result, k is an integer, and AA_(k), BB_(k),CC_(k) and DD_(k) are given by:

AA_(k)=(y_(k−0))²,

BB_(k)=(y_(k−) C0)²,

CC_(k)=(y_(k)−(C0+C1)² and

DD_(k)=(y_(k)−(2×C0+C1))²

|Pa−Pb|−(2×C0²+C1²) that satisfies Equations (18.1) and (18.2) isderived from the decoded result c_(k) and the standard deviation σ andaverage Pave are obtained from its distribution. Supposing thatdistribution is a normal distribution, the error probability is given bythe following Equation (19):

$\begin{matrix}{{P( {\sigma,{Pave}} )} = {{erfc}( \frac{Pave}{\sigma} )}} & (19)\end{matrix}$

Thus, the standard deviation σ and average Pave may be used to estimatethe error rate of the read signal or evaluate the quality of the readsignal.

As described above, even when a recorded code having a minimum polarityinversion interval of two is used in combination with the PR (C0, C1,C0) equalization, the quality of the read signal can also be evaluatedby the difference in probability |Pa−Pb| between the two paths of statetransitions occurring in a predetermined period.

Hereinafter, another specific preferred embodiment of the presentinvention will be described. In the following specific preferredembodiment, a recorded code having a minimum polarity inversion intervalof two is used as in the preferred embodiments described above. However,unlike the preferred embodiments described above, a PR (C0, C1, C2, C1,C0) (where C0, C1 and C2 are arbitrary positive integers) equalizationtechnique is applied to the following preferred embodiment.

Suppose recorded codes are denoted by:

Current recorded code: b_(k);

Recording code at the previous time: b_(k−1);

Recording code at the second last time: b_(k−2);

Recording code at the third last time: b_(k−3); and

Recording code at the fourth last time: b_(k−4)

An ideal value Level_(v) of a read signal that has been subjected to thePR (C0, C1, C2, C1, C0) equalization is given by the following Equation(20):

Level_(v) =C0×b _(k−4) +C1×b _(k−3) +C2×b _(k−2) +C1×b _(k−1) +C0×b_(k)  (20)

where k is an integer representing a time and v is an integer of 0 to 8.Supposing a state at a time k is identified by S (b_(k−3), b_(k−2),b_(k−1), b_(k)), a table of state transitions such as the followingTable 7 is obtained:

TABLE 7 State State S (b_(k−4), b_(k−3), S (b_(k−3), b_(k−2), b_(k−2),b_(k−1)) b_(k−1), b_(k)) at time k − 1 at time k b_(k)/LEVEL_(v) S (0,0, 0, 0) S (0, 0, 0, 0) 0/0 S (0, 0, 0, 0) S (0, 0, 0, 1) 1/C0 S (0, 0,0, 1) S (0, 0, 1, 1) 1/C0 + C1 S (0, 0, 1, 1) S (0, 1, 1, 0) 0/C1 + C2 S(0, 0, 1, 1) S (0, 1, 1, 1) 1/C0 + C1 + C2 S (0, 1, 1, 0) S (1, 1, 0, 0)0/C1 + C2 S (0, 1, 1, 1) S (1, 1, 1, 0) 0/2 * C1 + C2 S (0, 1, 1, 1) S(1, 1, 1, 1) 1/C0 + 2 * C1 + C2 S (1, 0, 0, 0) S (0, 0, 0, 0) 0/C0 S (1,0, 0, 0) S (0, 0, 0, 1) 1/2 * C0 S (1, 0, 0, 1) S (0, 0, 1, 1) 1/2 *C0 + C1 S (1, 1, 0, 0) S (1, 0, 0, 0) 0/C0 + C1 S (1, 1, 0, 0) S (1, 0,0, 1) 1/2 * C0 + C1 S (1, 1, 1, 0) S (1, 1, 0, 0) 0/C0 + C1 + C2 S (1,1, 1, 1) S (1, 1, 1, 0) 0/C0 + 2 * C1 + C2 S (1, 1, 1, 1) S (1, 1, 1, 1)1/2 * C0 + 2 * C1 + C2

In the following description, the states S (0, 0, 0, 0)_(k), S (0, 0, 0,1)_(k), S (0, 0, 1, 1)_(k), S (0, 1, 1, 1)_(k), S (1, 1, 1, 1)_(k), S(1, 1, 1, 0)_(k), S (1, 1, 0, 0)_(k), S (1, 0, 0, 0)_(k), S (1, 0, 0,1)_(k), S (0, 1, 1, 0)_(k) and so on at the time k will be identified byS0 _(k), S1 _(k), S2 _(k), S3 _(k), S4 _(k), S5 _(k, S6) _(k), S7 _(k),S8 _(k), S9 _(k) and so on, respectively, for the sake of simplicity.The state transitions that may occur in the period between the time k−1and the time k (i.e., a period of time corresponding to one cycle T of aread clock signal) are represented by the state transition diagram shownin FIG. 19. When the state transition diagram shown in FIG. 19 isexpanded with respect to the time axis, the trellis diagram shown inFIG. 20 is obtained.

In this preferred embodiment, each recorded code has a minimum polarityinversion interval of two and the PR (C0, C1, C2, C1, C0) equalizationtechnique is used. Under these conditions, there are 90 possible statetransition patterns (i.e., possible combinations of states) for statetransitions occurring from a predetermined state at a time into anotherpredetermined state at a different time along two paths (i.e., paths Aand B) as shown in the following Table 8:

TABLE 8 Recording Recording State code (b_(k−i), . . . , b_(k)) code(b_(k−i), . . . , b_(k)) transition of path A of path B S0_(k−5) →S6_(k) (0, 0, 0, 0, 0, 1, 1, 0, 0) (0, 0, 0, 0, 1, 1, 1, 0, 0) S0_(k−5)→ S5_(k) (0, 0, 0, 0, 0, 1, 1, 1, 0) (0, 0, 0, 0, 1, 1, 1, 1, 0)S0_(k−5) → S4_(k) (0, 0, 0, 0, 0, 1, 1, 1, 1) (0, 0, 0, 0, 1, 1, 1,1, 1) S2_(k−5) → S0_(k) (0, 0, 1, 1, 0, 0, 0, 0, 0) (0, 0, 1, 1, 1, 0,0, 0, 0) S2_(k−5) → S1_(k) (0, 0, 1, 1, 0, 0, 0, 0, 1) (0, 0, 1, 1, 1,0, 0, 0, 1) S2_(k−5) → S2_(k) (0, 0, 1, 1, 0, 0, 0, 1, 1) (0, 0, 1, 1,1, 0, 0, 1, 1) S3_(k−5) → S0_(k) (0, 1, 1, 1, 0, 0, 0, 0, 0) (0, 1, 1,1, 1, 0, 0, 0, 0) S3_(k−5) → S1_(k) (0, 1, 1, 1, 0, 0, 0, 0, 1) (0, 1,1, 1, 1, 0, 0, 0, 1) S3_(k−5) → S2_(k) (0, 1, 1, 1, 0, 0, 0, 1, 1) (0,1, 1, 1, 1, 0, 0, 1, 1) S7_(k−5) → S6_(k) (1, 0, 0, 0, 0, 1, 1, 0, 0)(1, 0, 0, 0, 1, 1, 1, 0, 0) S7_(k−5) → S5_(k) (1, 0, 0, 0, 0, 1, 1, 1,0) (1, 0, 0, 0, 1, 1, 1, 1, 0) S7_(k−5) → S4_(k) (1, 0, 0, 0, 0, 1, 1,1, 1) (1, 0, 0, 0, 1, 1, 1, 1, 1) S6_(k−5) → S6_(k) (1, 1, 0, 0, 0, 1,1, 0, 0) (1, 1, 0, 0, 1, 1, 1, 0, 0) S6_(k−5) → S5_(k) (1, 1, 0, 0, 0,1, 1, 1, 0) (1, 1, 0, 0, 1, 1, 1, 1, 0) S6_(k−5) → S4_(k) (1, 1, 0, 0,0, 1, 1, 1, 1) (1, 1, 0, 0, 1, 1, 1, 1, 1) S4_(k−5) → S0_(k) (1, 1, 1,1, 0, 0, 0, 0, 0) (1, 1, 1, 1, 1, 0, 0, 0, 0) S4_(k−5) → S1_(k) (1, 1,1, 1, 0, 0, 0, 0, 1) (1, 1, 1, 1, 1, 0, 0, 0, 1) S4_(k−5) → S2_(k) (1,1, 1, 1, 0, 0, 0, 1, 1) (1, 1, 1, 1, 1, 0, 0, 1, 1) S0_(k−6) → S0_(k)(0, 0, 0, 0, 0, 0, 0, 0, 0, (0, 0, 0, 0, 1, 1, 0, 0, 0, 0) 0) S0_(k−6) →S1_(k) (0, 0, 0, 0, 0, 0, 0, 0, 0, (0, 0, 0, 0, 1, 1, 0, 0, 0, 1) 1)S0_(k−6) → S2_(k) (0, 0, 0, 0, 0, 0, 0, 0, 1, (0, 0, 0, 0, 1, 1, 0, 0,1, 1) 1) S2_(k−6) → S6_(k) (0, 0, 1, 1, 0, 0, 1, 1, 0, (0, 0, 1, 1, 1,1, 1, 1, 0, 0) 0) S2_(k−6) → S5_(k) (0, 0, 1, 1, 0, 0, 1, 1, 1, (0, 0,1, 1, 1, 1, 1, 1, 1, 0) 0) S2_(k−6) → S4_(k) (0, 0, 1, 1, 0, 0, 1, 1, 1,(0, 0, 1, 1, 1, 1, 1, 1, 1, 1) 1) S3_(k−6) → S6_(k) (0, 1, 1, 1, 0, 0,1, 1, 0, (0, 1, 1, 1, 1, 1, 1, 1, 0, 0) 0) S3_(k−6) → S5_(k) (0, 1, 1,1, 0, 0, 1, 1, 1, (0, 1, 1, 1, 1, 1, 1, 1, 1, 0) 0) S3_(k−6) → S4_(k)(0, 1, 1, 1, 0, 0, 1, 1, 1, (0, 1, 1, 1, 1, 1, 1, 1, 1, 1) 1) S7_(k−6) →S0_(k) (1, 0, 0, 0, 0, 0, 0, 0, 0, (1, 0, 0, 0, 1, 1, 0, 0, 0, 0) 0)S7_(k−6) → S1_(k) (1, 0, 0, 0, 0, 0, 0, 0, 0, (1, 0, 0, 0, 1, 1, 0, 0,0, 1) 1) S7_(k−6) → S2_(k) (1, 0, 0, 0, 0, 0, 0, 0, 1, (1, 0, 0, 0, 1,1, 0, 0, 1, 1) 1) S6_(k−6) → S0_(k) (1, 1, 0, 0, 0, 0, 0, 0, 0, (1, 1,0, 0, 1, 1, 0, 0, 0, 0) 0) S6_(k−6) → S1_(k) (1, 1, 0, 0, 0, 0, 0, 0, 0,(1, 1, 0, 0, 1, 1, 0, 0, 0, 1) 1) S6_(k−6) → S2_(k) (1, 1, 0, 0, 0, 0,0, 0, 1, (1, 1, 0, 0, 1, 1, 0, 0, 1, 1) 1) S4_(k−6) → S6_(k) (1, 1, 1,1, 0, 0, 1, 1, 0, (1, 1, 1, 1, 1, 1, 1, 1, 0, 0) 0) S4_(k−6) → S5_(k)(1, 1, 1, 1, 0, 0, 1, 1, 1, (1, 1, 1, 1, 1, 1, 1, 1, 1, 0) 0) S4_(k−6) →S4_(k) (1, 1, 1, 1, 0, 0, 1, 1, 1, (1, 1, 1, 1, 1, 1, 1, 1, 1, 1) 1)S0_(k−7) → S0_(k) (0, 0, 0, 0, 0, 1, 1, 0, 0, (0, 0, 0, 0, 1, 1, 0, 0,0, 0, 0) 0, 0) S0_(k−7) → S1_(k) (0, 0, 0, 0, 0, 1, 1, 0, 0, (0, 0, 0,0, 1, 1, 0, 0, 0, 0, 1) 0, 1) S0_(k−7) → S2_(k) (0, 0, 0, 0, 0, 1, 1, 0,0, (0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1) 1, 1) S2_(k−7) → S6_(k) (0, 0, 1,1, 0, 0, 1, 1, 1, (0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0) 0, 0) S2_(k−7) →S5_(k) (0, 0, 1, 1, 0, 0, 1, 1, 1, (0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0) 1,0) S2_(k−7) → S4_(k) (0, 0, 1, 1, 0, 0, 1, 1, 1, (0, 0, 1, 1, 1, 0, 0,1, 1, 1, 1) 1, 1) S3_(k−7) → S6_(k) (0, 1, 1, 1, 0, 0, 1, 1, 1, (0, 1,1, 1, 1, 0, 0, 1, 1, 0, 0) 0, 0) S3_(k−7) → S5_(k) (0, 1, 1, 1, 0, 0, 1,1, 1, (0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0) 1, 0) S3_(k−7) → S4_(k) (0, 1,1, 1, 0, 0, 1, 1, 1, (0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1) 1, 1) S7_(k−7) →S0_(k) (1, 0, 0, 0, 0, 1, 1, 0, 0, (1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0) 0,0) S7_(k−7) → S1_(k) (1, 0, 0, 0, 0, 1, 1, 0, 0, (1, 0, 0, 0, 1, 1, 0,0, 0, 0, 1) 0, 1) S7_(k−7) → S2_(k) (1, 0, 0, 0, 0, 1, 1, 0, 0, (1, 0,0, 0, 1, 1, 0, 0, 0, 1, 1) 1, 1) S6_(k−7) → S0_(k) (1, 1, 0, 0, 0, 1, 1,0, 0, (1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0) 0, 0) S6_(k−7) → S1_(k) (1, 1,0, 0, 0, 1, 1, 0, 0, (1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1) 0, 1) S6_(k−7) →S2_(k) (1, 1, 0, 0, 0, 1, 1, 0, 0, (1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1)1, 1) S4_(k−7) → S6_(k) (1, 1, 1, 1, 0, 0, 1, 1, 1, (1, 1, 1, 1, 1, 0,0, 1, 1, 0, 0) 0, 0) S4_(k−7) → S5_(k) (1, 1, 1, 1, 0, 0, 1, 1, 1, (1,1, 1, 1, 1, 0, 0, 1, 1, 1, 0) 1, 0) S4_(k−7) → S4_(k) (1, 1, 1, 1, 0, 0,1, 1, 1, (1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1) 1, 1) S0_(k−8) → S0_(k) (0,0, 0, 0, 0, 1, 1, 1, 0, (0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0) 0, 0, 0)S0_(k−8) → S1_(k) (0, 0, 0, 0, 0, 1, 1, 1, 0, (0, 0, 0, 0, 1, 1, 1, 0,0, 0, 0, 1) 0, 0, 1) S0_(k−8) → S2_(k) (0, 0, 0, 0, 0, 1, 1, 1, 0, (0,0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1) 0, 1, 1) S2_(k−8) → S6_(k) (0, 0, 1, 1,0, 0, 0, 1, 1, (0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0) 1, 0, 0) S2_(k−8) →S5_(k) (0, 0, 1, 1, 0, 0, 0, 1, 1, (0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0)1, 1, 0) S2_(k−8) → S4_(k) (0, 0, 1, 1, 0, 0, 0, 1, 1, (0, 0, 1, 1, 1,0, 0, 0, 1, 1, 1, 1) 1, 1, 1) S3_(k−8) → S6_(k) (0, 1, 1, 1, 0, 0, 0, 1,1, (0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0) 1, 0, 0) S3_(k−8) → S5_(k) (0,1, 1, 1, 0, 0, 0, 1, 1, (0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0) 1, 1, 0)S3_(k−8) → S4_(k) (0, 1, 1, 1, 0, 0, 0, 1, 1, (0, 1, 1, 1, 1, 0, 0, 0,1, 1, 1, 1) 1, 1, 1) S7_(k−8) → S0_(k) (1, 0, 0, 0, 0, 1, 1, 1, 0, (1,0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0) 0, 0, 0) S7_(k−8) → S1_(k) (1, 0, 0, 0,0, 1, 1, 1, 0, (1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1) 0, 0, 1) S7_(k−8) →S2_(k) (1, 0, 0, 0, 0, 1, 1, 1, 0, (1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1)0, 1, 1) S6_(k−8) → S0_(k) (1, 1, 0, 0, 0, 1, 1, 1, 0, (1, 1, 0, 0, 1,1, 1, 0, 0, 0, 0, 0) 0, 0, 0) S6_(k−8) → S1_(k) (1, 1, 0, 0, 0, 1, 1, 1,0, (1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1) 0, 0, 1) S6_(k−8) → S2_(k) (1,1, 0, 0, 0, 1, 1, 1, 0, (1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1) 0, 1, 1)S4_(k−8) → S6_(k) (1, 1, 1, 1, 0, 0, 0, 1, 1, (1, 1, 1, 1, 1, 0, 0, 0,1, 1, 0, 0) 1, 0, 0) S4_(k−8) → S5_(k) (1, 1, 1, 1, 0, 0, 0, 1, 1, (1,1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0) 1, 1, 0) S4_(k−8) → S4_(k) (1, 1, 1, 1,0, 0, 0, 1, 1, (1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1) 1, 1, 1) S0_(k−9) →S0_(k) (0, 0, 0, 0, 0, 1, 1, 1, 1, (0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0,0) 0, 0, 0, 0) S0_(k−9) → S1_(k) (0, 0, 0, 0, 0, 1, 1, 1, 1, (0, 0, 0,0, 1, 1, 1, 1, 0, 0, 0, 0, 1) 0, 0, 0, 1) S0_(k−9) → S2_(k) (0, 0, 0, 0,0, 1, 1, 1, 1, (0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1) 0, 0, 1, 1)S2_(k−9) → S6_(k) (0, 0, 1, 1, 0, 0, 0, 0, 1, (0, 0, 1, 1, 1, 0, 0, 0,0, 1, 1, 0, 0) 1, 1, 0, 0) S2_(k−9) → S5_(k) (0, 0, 1, 1, 0, 0, 0, 0, 1,(0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0) 1, 1, 1, 0) S2_(k−9) → S4_(k)(0, 0, 1, 1, 0, 0, 0, 0, 1, (0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1) 1,1, 1, 1) S3_(k−9) → S6_(k) (0, 1, 1, 1, 0, 0, 0, 0, 1, (0, 1, 1, 1, 1,0, 0, 0, 0, 1, 1, 0, 0) 1, 1, 0, 0) S3_(k−9) → S5_(k) (0, 1, 1, 1, 0, 0,0, 0, 1, (0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0) 1, 1, 1, 0) S3_(k−9) →S4_(k) (0, 1, 1, 1, 0, 0, 0, 0, 1, (0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1,1, 1) 1, 1, 1, 1) S7_(k−9) → S0_(k) (1, 0, 0, 0, 0, 1, 1, 1, 1, (1, 0,0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0) 0, 0, 0, 0) S7_(k−9) → S1_(k) (1, 0, 0,0, 0, 1, 1, 1, 1, (1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1) 0, 0, 0, 1)S7_(k−9) → S2_(k) (1, 0, 0, 0, 0, 1, 1, 1, 1, (1, 0, 0, 0, 1, 1, 1, 1,0, 0, 0, 1, 1) 0, 0, 1, 1) S6_(k−9) → S0_(k) (1, 1, 0, 0, 0, 1, 1, 1, 1,(1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0) 0, 0, 0, 0) S6_(k−9) → S1_(k)(1, 1, 0, 0, 0, 1, 1, 1, 1, (1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1) 0,0, 0, 1) S6_(k−9) → S2_(k) (1, 1, 0, 0, 0, 1, 1, 1, 1, (1, 1, 0, 0, 1,1, 1, 1, 0, 0, 0, 1, 1) 0, 0, 1, 1) S4_(k−9) → S6_(k) (1, 1, 1, 1, 0, 0,0, 0, 1, (1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0) 1, 1, 0, 0) S4_(k−9) →S5_(k) (1, 1, 1, 1, 0, 0, 0, 0, 1, (1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1,0) 1, 1, 1, 0) S4_(k−9) → S4_(k) (1, 1, 1, 1, 0, 0, 0, 0, 1, (1, 1, 1,1, 1, 0, 0, 0, 0, 1, 1, 1, 1) 1, 1, 1, 1)

In this case, it is determined which of the two paths A and B has thehigher probability. This decision can be made by comparing the sum oferrors between ideal sample values (i.e., expected values) shown by thepath A and actual sample values with the sum of errors betweenassociated ideal sample values (i.e., expected values) shown by the pathB and the actual sample values.

For example, suppose the state transition S0 _(k−5)→S6 _(k) should beestimated. As for this state transition, no matter whether the path A orthe path B has been taken, the state at the time k−5 is S0 _(k−5) andthe state at the time k is S6 _(k). In this case, it is by using the sumof squared errors between the expected values and the actual valuesy_(k−4), y_(k−3), y_(k−2), y_(k−1), and y_(k) of the read signal in theperiod between the times k−4 and k that it is determined which of thetwo paths A and B has the higher probability. As in the preferredembodiments described above, the sum of squared errors between theexpected values shown by the path A and the actual values y_(k−4),y_(k−3), y_(k−2), y_(k−1), and y_(k) of the read signal in the periodbetween the times k−4 and k is identified by Pa. On the other hand, thesum of squared errors between the expected values shown by the path Band the actual values y_(k−4), y_(k−3), y_(k−2), y_(k−1) and y_(k) ofthe read signal in the period between the times k−4 and k is identifiedby Pb. These sums of squared errors Pa and Pb (i.e., the errorprobabilities) are respectively given by the following Equations (21)and (22):

Pa=(y _(k−4)−0)²+(y _(k−3) −C0)²+(y _(k−2)−(C0+C1))²+(y_(k−1)−(C0+C1+C2))²+(y _(k)−(2×C1+C2))²  (21)

Pb=(y _(k−4) −C0)²+(y _(k−3)−(C0+C1))²(y _(k−2)−(C0+C1C2))²+(y_(k−1)−(C0+2×C1+C2))²+(y _(k)−(C0+2×C1+C2))²  (22)

In this case, if Pa<<Pb, then the path A is estimated to be the moreprobable one. On the other hand, if Pa>>Pb, then the path B is estimatedto be the more probable one. That is to say, even when a recorded codehaving a minimum polarity inversion interval of two is combined with thePR (C0, C1, C2, C1, C0) equalization technique, the reliability of thedecoded result can also be evaluated by |Pa−Pb|. Also, the quality ofthe read signal can be evaluated (or the error rate can be estimated)based on the |Pa−Pb| distribution.

Furthermore, suppose white noise has been superposed on the transmissionline. In that case, a state transition having the highest errorprobability should have a minimum Euclidean distance between the paths Aand B. The eighteen state transition patterns shown in the following

Table 9 should have the minimum Euclidean distance between their twopaths:

TABLE 9 State Recording code Recording code transition (b_(k−i), . . . ,b_(k)) of path A (b_(k−i), . . . , b_(k)) of path B S0_(k−5) → S6_(k)(0, 0, 0, 0, 0, 1, 1, 0, 0) (0, 0, 0, 0, 1, 1, 1, 0, 0) S0_(k−5) →S5_(k) (0, 0, 0, 0, 0, 1, 1, 1, 0) (0, 0, 0, 0, 1, 1, 1, 1, 0) S0_(k−5)→ S4_(k) (0, 0, 0, 0, 0, 1, 1, 1, 1) (0, 0, 0, 0, 1, 1, 1, 1, 1)S2_(k−5) → S0_(k) (0, 0, 1, 1, 0, 0, 0, 0, 0) (0, 0, 1, 1, 1, 0, 0, 0,0) S2_(k−5) → S1_(k) (0, 0, 1, 1, 0, 0, 0, 0, 1) (0, 0, 1, 1, 1, 0, 0,0, 1) S2_(k−5) → S2_(k) (0, 0, 1, 1, 0, 0, 0, 1, 1) (0, 0, 1, 1, 1, 0,0, 1, 1) S3_(k−5) → S0_(k) (0, 1, 1, 1, 0, 0, 0, 0, 0) (0, 1, 1, 1, 1,0, 0, 0, 0) S3_(k−5) → S1_(k) (0, 1, 1, 1, 0, 0, 0, 0, 1) (0, 1, 1, 1,1, 0, 0, 0, 1) S3_(k−5) → S2_(k) (0, 1, 1, 1, 0, 0, 0, 1, 1) (0, 1, 1,1, 1, 0, 0, 1, 1) S7_(k−5) → S6_(k) (1, 0, 0, 0, 0, 1, 1, 0, 0) (1, 0,0, 0, 1, 1, 1, 0, 0) S7_(k−5) → S5_(k) (1, 0, 0, 0, 0, 1, 1, 1, 0) (1,0, 0, 0, 1, 1, 1, 1, 0) S7_(k−5) → S4_(k) (1, 0, 0, 0, 0, 1, 1, 1, 1)(1, 0, 0, 0, 1, 1, 1, 1, 1) S6_(k−5) → S6_(k) (1, 1, 0, 0, 0, 1, 1, 0,0) (1, 1, 0, 0, 1, 1, 1, 0, 0) S6_(k−5) → S5_(k) (1, 1, 0, 0, 0, 1, 1,1, 0) (1, 1, 0, 0, 1, 1, 1, 1, 0) S6_(k−5) → S4_(k) (1, 1, 0, 0, 0, 1,1, 1, 1) (1, 1, 0, 0, 1, 1, 1, 1, 1) S4_(k−5) → S0_(k) (1, 1, 1, 1, 0,0, 0, 0, 0) (1, 1, 1, 1, 1, 0, 0, 0, 0) S4_(k−5) → S1_(k) (1, 1, 1, 1,0, 0, 0, 0, 1) (1, 1, 1, 1, 1, 0, 0, 0, 1) S4_(k−5) → S2_(k) (1, 1, 1,1, 0, 0, 0, 1, 1) (1, 1, 1, 1, 1, 0, 0, 1, 1)

The reliabilities Pa−Pb of the 18 state transition patterns shown inTable 9 are given by the following Equations (23.1) through (23.18):

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,0,0,0,x,1,1,0,0), then Pa−Pb=(AA _(k−4) −BB_(k−4))+(BB _(k−3) −CC _(k−3))+(CC _(k−2) −EE _(k−2))+(DD _(k−1) −FF_(k−1))+(DD _(k) −EE _(k));  (23.1)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,0,0,0,x,1,1,1,0), then Pa−Pb=(AA _(k−4) −BB_(k−4))+(BB _(k−3) −CC _(k−3))+(CC _(k−2) −EE _(k−2))+(EE _(k−1) −GG_(k−1))+(FF _(k) −GG _(k));  (23.2)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,0,0,0, x,1,1,1,1), then Pa−Pb=(AA _(k−4) −BB_(k−4))+(BB _(k−3) −CC _(k−3))+(CC _(k−2) −EE _(k−2))+(EE _(k−1) −GG_(k−1))+(GG_(k) −JJ _(k));  (23.3)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,0,1,1,x,0,0,0,0), then Pa−Pb=(DD _(k−4) −EE_(k−4))+(DD _(k−3) −FF _(k−3))+(CC _(k−2) −EE _(k−2))+(BB _(k−1) −CC_(k−1))+(AA _(k) −BB _(k));  (23.4)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,0,1,1,x,0,0,0,1), then Pa−Pb=(DD _(k−4) −EE_(k−4))+(DD _(k−3) −FF _(k−3))+(CC _(k−2) −EE _(k−2))+(BB _(k−1) −CC_(k−1))+(BB _(k) −HH _(k));  (23.5)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,0,1,1,x,0,0,1,1), then Pa−Pb=(DD _(k−4) −EE_(k−4))+(DD _(k−3) −FF _(k−3))+(CC _(k−2) −EE _(k−2))+(HH _(k−1) −II_(k−1))+(CC _(k) −II _(k));  (23.6)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,1,1,1,x,0,0,0,0), then Pa−Pb=(FF _(k−4) −GG_(k−4))+(EE _(k−3) −GG _(k−3))+(CC _(k−2) −EE _(k−2))+(BB _(k−1) −CC_(k−1))+(AA _(k) −BB _(k));  (23.7)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,1,1,1,x,0,0,0,1), then Pa−Pb=(FF _(k−4) −GG_(k−4))+(EE _(k−3) −GG _(k−3))+(CC _(k−2) −EE _(k−2))+(BB _(k−1) −CC_(k−1))+(BB _(k) −HH _(k));  (23.8)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,1,1,1,x,0,0,1,1), then Pa−Pb=(FF _(k−4) −GG_(k−4))+(EE _(k−3) −GG _(k−3))+(CC _(k−2) −EE _(k−2))+(HH _(k−1) −II_(k−1))+(CC _(k) −II _(k));  (23.9)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(1,0,0,0,x,1,1,0,0), then Pa−Pb=(BB _(k−4) −HH_(k−4))+(BB _(k−3) −CC _(k−3))+(CC _(k−2) −EE _(k−2))+(DD _(k−1) −FF_(k−1))+(DD _(k) −EE _(k));  (23.10)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(1,0,0,0,x,1,1,1,0), then Pa−Pb=(BB _(k−4) −HH_(k−4))+(BB _(k−3) −CC _(k−3))+(CC _(k−2) −EE _(k−2))+(EE _(k−1) −GG_(k−1))+(FF _(k) −GG _(k));  (23.11)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(1,0,0,0,x,1,1,1,1), then Pa−Pb=(BB _(k−4) −HH_(k−4))+(BB _(k−3) −CC _(k−3))+(CC _(k−2) −EE _(k−2))+(EE _(k−1) −GG_(k−1))+(GG _(k) −JJ _(k));  (23.12)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(1,1,0,0,x,1,1,0,0), then Pa−Pb=(CC _(k−4) −II_(k−4))+(HH _(k−3) −II _(k−3))+(CC _(k−2) −EE _(k−2))+(DD _(k−1) −FF_(k−1))+(DD _(k) −EE _(k));  (23.13)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(1,1,0,0,x,1,1,1,0), then Pa−Pb=(CC _(k−4) −II_(k−4))+(HH _(k−3) −II _(k−3))+(CC _(k−2) −EE _(k−2))+(EE _(k−1) −GG_(k−1))+(FF _(k) −GG _(k));  (23.14)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(1,1,0,0,x,1,1,1,1), then Pa−Pb=(CC _(k−4) −II_(k−4))+(HH _(k−3) −II _(k−3))+(CC _(k−2) −EE _(k−2))+(EE _(k−1) −GG_(k−1))+(GG _(k) −JJ _(k));  (23.15)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(1,1,1,1,x,0,0,0,0), then Pa−Pb=(GG _(k−4) −JJ_(k−4))+(EE _(k−3) −GG _(k−3))+(CC _(k−2) −EE _(k−2))+(BB _(k−1) −CC_(k−1))+(AA _(k) −BB _(k));  (23.16)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(1,1,1,1,x,0,0,0,1), then Pa−Pb=(GG _(k−4) −JJ_(k−4))+(EE _(k−3) −GG _(k−3))+(CC _(k−2) −EE _(k−2))+(BB _(k−1) −CC_(k−1))+(BB _(k) −HH _(k)); and  (23.17)

If (c _(k−8) ,c _(k−7) ,c _(k−6) ,c _(k−5) ,c _(k−4) ,c _(k−3) ,c _(k−2),c _(k−1) ,c _(k))=(0,1,1,1,x,0,0,1,1), then Pa−Pb=(GG _(k−4) −JJ_(k−4))+(EE _(k−3) −GG _(k−3))+(CC _(k−2) −EE _(k−2))+(HH _(k−1) −II_(k−1))+(CC _(k) −II _(k)).  (23.18)

where c_(k) is the decoded result, k is an integer and AA_(k), BB_(k),CC_(k), DD_(k), EE_(k), FF_(k), GG_(k), HH_(k), II_(k) and JJ_(k) aregiven by:

AA_(k)=(y_(k)−0)²,

BB_(k)=(y_(k)−C0)²,

CC_(k)=(y_(k)−(C0+C1))²,

DD_(k)=(y_(k)−(C1+C2))²,

EE_(k)=(y_(k)−(C0+C1+C2)²,

FF_(k)=(y_(k)−(2×C1+C2))²,

GG_(k)=(y_(k)−(C0+2×C1+C2))²,

HH_(k)=(y_(k)−2×C0))²,

II_(k)=(y_(k)−(2×C0+C1))² and

JJ_(k)=(y_(k)−(2×C0+2×C1+C2))²

|Pa−Pb|−(2×C0²+2×C1²+C2²) that satisfies Equations (23.1) through(23.18) is derived from the decoded result c_(k) and the standarddeviation σ and average Pave are obtained from its distribution.Supposing that distribution is a normal distribution, the errorprobability is given by the following Equation (24):

$\begin{matrix}{{P( {\sigma,{Pave}} )} = {{erfc}( \frac{Pave}{\sigma} )}} & (24)\end{matrix}$

Thus, the standard deviation σ and average Pave may be used to estimatethe error rate of the read signal or evaluate the quality of the readsignal.

As described above, even when a recorded code having a minimum polarityinversion interval of two is used in combination with the PR (C0, C1,C2, C1, C0) equalization, the quality of the read signal can also beevaluated by the difference in probability |Pa−Pb| between the two pathsof state transitions occurring in a predetermined period.

Embodiment 2

Hereinafter, a second specific preferred embodiment of the presentinvention will be described. The second preferred embodiment relates toa specific method of calculating the probabilities of respective statesand the reliability Pa−Pb of the decoded result where the read signal isdecoded by a PRML decoding method (e.g., the PR (1, 2, 2, 1)equalization technique described above).

As described above, when the PR (1, 2, 2, 1) equalization technique isadopted, a trellis diagram such as that shown in FIG. 4 is obtained. Inthe preferred embodiment described above, the probabilities L_(k) ^(S0)through L_(k) ^(S5) of the respective states S0 through S5 at the time kare given by the following Equations (25):

L _(k) ^(S0)=min[L _(k−1) ^(S0)+(y _(k)+3)²/2−y _(k) ²/2, L _(k−1)^(S5)+(y _(k)+2)²/2−y _(k) ²/2]

L _(k) ^(S1)=min[L _(k−1) ^(S0)+(y _(k)+2)²/2−y _(k) ²/2, L _(k−1)^(S5)+(y _(k)+1)²/2−y _(k) ²/2]

L _(k) ^(S2) =L _(k−1) ^(S1)+(y _(k)+0)²

L _(k) ^(S3)=min[L _(k−1) ^(S3)+(y _(k)−3)² , L _(k−1) ^(S2)+(y_(k)−2)²]

L _(k) ^(S4)=min[L _(k−1) ^(S3)+(y _(k)−2)² , L _(k−1) ^(S2)+(y_(k)−1)²]

L _(k) ^(S5) =L _(k−1) ^(S4)+(y _(k)+0)²  (25)

where L_(k−1) ^(S0) through L_(k−1) ^(S5) are the probabilities of therespective states S0 through S5 at the previous time k−1, y_(k) is theactual sample value at the time k, and min [xxx, zzz] is an operatorindicating that the smaller one of xxx and zzz should be selected.

In this preferred embodiment, however, each branch metric (e.g.,(y_(k)+3)²) to be added to its associated probability (e.g., L_(k−1)^(S0)) at the previous time k−1 is always divided by two and then y_(k)²/2 is always subtracted from the sum. In the PRML decoding method, thesmallest one of the probabilities L_(k) ^(S0) through L_(k) ^(S5) may beselected by comparing them with each other. Accordingly, if thesecalculation rules are applied to all of the equations for obtainingL_(k) ^(S0) through L_(k) ^(S5), then the decoded result will not beaffected at all. Thus, the probabilities L_(k) ^(S0) through L_(k) ^(S5)of the respective states S0 through S5 at the time k may be given by thefollowing Equations (26):

L _(k) ^(S0)=min[L _(k−1) ^(S0)+(y _(k)+3)²/2−y _(k) ²/2, L _(k−1)^(S5)+(y _(k)+2)²/2−y _(k) ²/2]

L _(k) ^(S1)=min[L _(k−1) ^(S0)+(y _(k)+2)²/2−y _(k) ²/2, L _(k−1)^(S5)+(y _(k)+1)²/2−y _(k) ²/2]

L _(k) ^(S2) =L _(k−1) ^(S1)+(y _(k)+0)²/2−y _(k) ²/2

L _(k) ^(S3)=min[L _(k−1) ^(S3)+(y _(k)−3)²/2−y _(k) ²/2, L _(k−1)^(S2)+(y _(k)−2)²/2−y _(k) ²/2]

L _(k) ^(S4)=min[L _(k−1) ^(S3)+(y _(k)−2)²/2−y _(k) ²/2, L _(k−1)^(S2)+(y _(k)−1)²/2−y _(k) ²/2]

L _(k) ^(S5) =L _(k−1) ^(S4)+(y _(k)+0)²/2−y _(k) ²/2  (26)

These Equations (26) may be expanded into the following Equations (27):

L _(k) ^(S0)=min[L _(k−1) ^(S0)+3y _(k)+9/2, L _(k−1) ^(S5)+2y _(k)+2]

L _(k) ^(S1)=min[L _(k−1) ^(S0)+2y _(k)+2, L _(k−1) ^(S5) +y _(k)+1/2]

L _(k) ^(S2)=minL _(k−1) ^(S1)

L _(k) ^(S3)=min[L _(k−1) ^(S3)−3y _(k)+9/2, L _(k−1) ^(S2)−2y _(k)+2]

L _(k) ^(S4)=min[L _(k−1) ^(S3)−2y _(k)+2, L _(k−1) ^(S2)−1/2]

L _(k) ^(S5) =L _(k−1) ^(S4)  (27)

In this case, A_(k), B_(k), C_(k), D_(k), E_(k), F_(k) and G_(k) aredefined as follows:

A _(k)=3y _(k)+9/2=(y _(k) −th4)+(y _(k) −th5)+(y _(k) −th6)

B _(k)=2y _(k)2=(y _(k) −th4)+(y _(k) −th5)

C _(k) =y _(k)+1/2=(y _(k) −th4)

E _(k) =−y _(k)+1/2=(th3−y _(k))

F _(k)=−2y _(k)+2=(th3−y _(k))+(th2−y _(k))

G _(k)=−3y _(k)+9/2=(th3−y _(k))+(th2−y _(k))+(th1−y _(k))

where th1=5/2, th2=3/2, th3=1/2, th4=−1/2, th5=−3/2 and th6=−5/2.

In this manner, when the sample value y_(k) is detected at the time k,the probabilities L_(k) ^(S0) through L_(k) ^(S5) of the respectivestates S0 through S5 at the time k may be obtained by calculating A_(k)through G_(k) through simple multiplications and additions following theEquations (27), i.e., without calculating the squared errors between theideal values and the actual sample values. Thus, the circuitconfiguration of the ML decoder does not have to be so complicated.

As already described for the first preferred embodiment, the quality ofthe read signal may be evaluated by obtaining the difference inprobability |Pa−Pb| between two possible state transition paths (i.e.,paths A and B). However, this |Pa−Pb| calculation may also be arelatively simple one that includes no square calculations. Hereinafter,an alternative simplified method of calculating |Pa−Pb| will bedescribed specifically.

In the first preferred embodiment described above, where the PR (1, 2,2, 1) equalization technique is adopted, the Pa−Pb values are preferablyobtained for such pairs of paths A and B as having the minimum Euclideandistance between them. As for the 16 state transitions shown in Table 2,for example, the Pa−Pb values are preferably obtained for the eightstate transitions that result in Pa−Pb=±10 when Pa=0 or Pb=0.

For example, the Pa−Pb value may be obtained in the following manner forthe S0 _(k−4)→S4 _(k) transition, which is one of those eight statetransitions resulting in Pa−Pb=4±10. In this case, the path A includesstate transitions of S0→S0→S1→S2→S4 and the path B includes statetransitions of S0→S1→S2→S3→S4. Then, the probability Pa of the path Amay be given by:

Pa=(y _(k−3)+3)²/2+(y _(k−2)+2)²/2+(y _(k−1)+0)²/2+(y _(k)−1)²/2

n the other hand, the probability Pb of the path B may be given by:

Pb=(y _(k−3)+2)²/2+(y _(k−2)+0)²/2+(y _(k−1)−2)²/2+(y _(k)−2)²/2

In this case, by using the A_(k) through G_(k) values, the Pa−Pb may beobtained by:

Pa−Pb=(A _(k−3) −B _(k−3))+B _(k−2) −F _(k−1)+(E _(k) −F _(k))

In this manner, according to this preferred embodiment, the Pa−Pb valuecan be calculated by using the A_(k) through G_(k) values that areobtained through simple additions and subtractions on the sample valuey_(k) and the preset values th1 through th6. Thus, the Pa−Pb value canbe obtained relatively easily without performing the squarecalculations. As a result, the ML decoder may have a simplified circuitconfiguration.

The Pa−Pb values may also be calculated by using the A_(k) through G_(k)values in a similar manner for the other state transitions. The Pa−Pbvalues of some of the other state transitions may be obtained in thefollowing manner:

As for state transition S0 _(k−4)→S3 _(k):

Pa−Pb=(A _(k−3) −B _(k−3))+B _(k−2) −F _(k−1)+(F _(k) −G _(k))

As for state transition S2 _(k−4)→S0 _(k):

Pa−Pb=(E _(k−3) −F _(k−3))−F _(k−2) +B _(k−1)+(A _(k) −B _(k))

As for state transition S2 _(k−4)→S1 _(k):

Pa−Pb=(E _(k−3) −F _(k−3))−F _(k−2) +B _(k−1)+(B _(k) −C _(k))

As for state transition S5 _(k−4)→S4 _(k):

Pa−Pb=(B _(k−3) −C _(k−3))+B _(k−2) −F _(k−1)+(E _(k) −F _(k))

As for state transition S5 _(k−4)→S3 _(k):

Pa−Pb=(B _(k−3) −C _(k−3))+B _(k−2) −F _(k−1)+(F _(k) −G _(k))

As for state transition S3 _(k−4)→S0 _(k):

Pa−Pb=(F _(k−3) −G _(k−3))−F _(k−2) +B _(k−1)+(A _(k) −B _(k))

As for state transition S3 _(k−4)→S1 _(k):

Pa−Pb=(F _(k−3) −G _(k−3))−F _(k−2) +B _(k−1)+(B _(k) −C _(k))

Embodiment 3

Hereinafter, a third specific preferred embodiment of the presentinvention will be described with reference to FIG. 7. The thirdpreferred embodiment relates to an optical disk drive 100 for use todecode a read signal by a PRML decoding method.

In the optical disk drive 100, a read signal, which has been read outfrom an optical disk 8 by an optical head 50, is amplified by apreamplifier 9. The pre-amplified signal is subjected to AC coupling andthen input to an automatic gain controller (AGC) 10. The AGC 10 controlsthe gain of its input signal so that the output of a waveform equalizer11 on the next stage will have predetermined amplitude. Thegain-controlled output signal of the AGC 10 has its waveform shaped bythe waveform equalizer 11. Then, the waveform-shaped output signal ofthe waveform equalizer 11 is supplied to both a PLL circuit 12 and anA/D converter 13.

The PLL circuit 12 generates a read clock signal that is synchronizedwith the read signal. The PLL circuit 12 may have the same configurationas the conventional PLL circuit shown in FIG. 1 (including the phasedetector 5, LPF 6 and VCO 7). In response to the read clock signal thatis supplied from the PLL circuit 12, the A/D converter 13 samples theread signal. The A/D converter 13 outputs the sampled data obtained inthis manner to a digital filter 14.

The digital filter 14 has a frequency characteristic that has beendefined so as to match the frequency characteristic of the read/writesystems with the characteristic required by a Viterbi circuit 15. Inthis preferred embodiment, the characteristic required by the Viterbicircuit 15 is a PR (1, 2, 2, 1) equalization characteristic. The outputfiltered data of the digital filter 14 is input to the Viterbi circuit15, which decodes the data by a maximum likelihood decoding method. Morespecifically, the Viterbi circuit 15 decodes the PR (1, 2, 2, 1)equalized signal by the maximum likelihood decoding, thereby outputtingdigital-data.

The Viterbi circuit 15 outputs not only the decoded digital data butalso Euclidean distances that have been calculated at respective pointsin time (i.e., branch metrics) to a differential metric analyzer 16. Thedifferential metric analyzer 16 estimates possible state transitionsfrom the digital data that has been supplied from the Viterbi circuit15. Also, the differential metric analyzer 16 derives Pa−Pb,representing the reliability of the decoded result, from the estimatedstate transitions and the branch metrics, thereby estimating the errorrate of the decoded result.

Hereinafter, the Viterbi circuit 15 and the differential metric analyzer16 will be described in further detail with reference to FIG. 8. FIG. 8is a block diagram illustrating an exemplary configuration for theViterbi circuit 15 and differential metric analyzer 16. Sample valuesy_(k) that have been output from the digital filter 14 are input to abranch metric calculator 17 of the Viterbi circuit 15. The branch metriccalculator 17 calculates respective branch metrics corresponding to thedistances between the sample values y_(k) and their associated expectedvalues Level_(v). Since the PR (1, 2, 2, 1) equalization technique isadopted in this preferred embodiment, the expected values Level_(v) haveseven values of 0 through 6. The branch metrics A_(k), B_(k), C_(k),D_(k), E_(k), F_(k) and G_(k) representing the respective distancesbetween the expected values and sample values y_(k) at the time k aredefined by the following Equations (28):

A _(k)=(y _(k)−0)²,

B _(k)=(y _(k)−1)²,

C _(k)=(y _(k)−2)²,

D _(k)=(y _(k)−3)²,

E _(k)=(y _(k)−3)²,

F _(k)=(y _(k)−5)² and

G _(k)=(y _(k)−6)²  (28)

The branch metrics that have been calculated in this manner are input toan adder/comparator/selector 18. The probabilities (i.e., metric values)of the respective states S0 through S5 (see FIG. 4) at a current time kare obtained from the branch metrics at the current time k and theprobabilities of those states S0 through S5 at the previous time k−1.The probabilities of the respective states S0 through S5 at the currenttime k are given by the following Equations (29):

L _(k) ^(S0)=min[L _(k−1) ^(S0) +A _(k) , L _(k−1) ^(S5) +B _(k)]

L _(k) ^(S1)=min[L _(k−1) ^(S0) +B _(k) , L _(k−1) ^(S5) +C _(k)]

L _(k) ^(S2) =L _(k−1) ^(S1) +D _(k)

L _(k) ^(S3)=min[L _(k−1) ^(S3) +G _(k) , L _(k−1) ^(S2) +F _(k)]

L _(k) ^(S4)=min[L _(k−1) ^(S3) +F _(k) , L _(k−1) ^(S2) +E _(k)]

L _(k) ^(S5) =L _(k−1) ^(S4) +D _(k)  (29)

where min [xxx, zzz] is an operator indicating that the smaller one ofthe two values xxx and zzz should be selected. The metric values L_(k)^(S0) through L_(k) ^(S5) at the time k are stored in a register 19 andwill be used to calculate metric values of the respective states S0through S5 at the next time k+1. The adder/comparator/selector 18selects state transitions that have the minimum metric values inaccordance with Equations (29). Also, based on the results of selection,the adder/comparator/selector 18 outputs control signals Se10 throughSe13 to a path memory 20, which has a circuit configuration such as thatshown in FIG. 9, in accordance with the following Inequalities (30):

If L _(k−1) ^(S0) +A _(k) ≧L _(k−1) ^(S5) +B _(k), then Sel0=“1”

If L _(k−1) ^(S0) +A _(k) ≧L _(k−1) ^(S5) +B _(k), then Sel0=“1”

If L _(k−1) ^(S0) +A _(k) <L _(k−1) ^(S5) +B _(k), then Sel0=“0”

If L _(k−1) ^(S0) +B _(k) ≧L _(k−1) ^(S5) +C _(k), then Sel1=“1”

If L _(k−1) ^(S0) +B _(k) <L _(k−1) ^(S5) +C _(k), then Sel1=“0”

If L _(k−1) ^(S3) +G _(k) ≧L _(k−1) ^(S2) +F _(k), then Sel2=“1”

If L _(k−1) ^(S3) +G _(k) <L _(k−1) ^(S2) +F _(k), then Sel2=“0”

If L _(k−1) ^(S3) +F _(k) ≧L _(k−1) ^(S2) +E _(k), then Sel3=“1”

If L _(k−1) ^(S3) +F _(k) <L _(k−1) ^(S2) +E _(k), then Sel3=“0”

In response to the input control signals, the path memory 20 estimatesmost probable state transition paths according to the state transitionrule and outputs digital decoded data c_(k) corresponding to theestimated state transition paths.

On the other hand, to evaluate the quality of the read signal, thebranch metrics that have been output from the branch metric calculator17 are input to a delay circuit 21. The output of the branch metrics toa differential metric calculator 22 is delayed for the amount of timecorresponding to the time it takes for the adder/comparator/selector 18and the path memory 20 to perform their signal processing. In themeantime, the output digital data c_(k) of the path memory 20 is inputto a state transition detector 23, which detects predetermined patternsfrom the digital data c_(k). Specifically, the state transition detector23 detects data patterns corresponding to the eight state transitionsgiven by Equations (9.1) though (9.8). When the state transitiondetector 23 detects the predetermined state transitions, thedifferential metric calculator 22 calculates the Pa−Pb values of thosedetected state transitions in accordance with the Equations (9.1)through (9.8).

It should be noted that the Pa−Pb values may be calculated by a methodincluding no square calculations as described for the second preferredembodiment. In the method of the second preferred embodiment, the Pa−Pbvalues may be obtained without using the branch metrics that have beencalculated by the branch metric calculator 17. Accordingly, in thatcase, the sample values y_(k) that have been output from the digitalfilter 14 may be directly input to the differential metric calculator 22by way of the delay circuit 21 only. The differential metric calculator22 may obtain the Pa−Pb values from the sample values y_(k) by themethod described for the second preferred embodiment.

The Pa−Pb values that have been calculated in this manner for thepredetermined state transitions detected are input to anaverage/standard deviation calculator 24. The average/standard deviationcalculator 24 obtains and outputs the average Pave₁₀, and the standarddeviation σ₁₀ of the distribution of the input Pa−Pb values. It shouldbe noted that the average Pave₁₀ and the standard deviation σ₁₀ to beoutput in this case are obtained for predetermined state transitions,each having two possible paths with a minimum Euclidean distance betweenthem (i.e., having relatively high error probabilities). According toEquation (11), the error rate of the read signal can be estimated byusing the average Pave₁₀ and the standard deviation σ₁₀. That is to say,the standard deviation and the average obtained by the average/standarddeviation calculator 24 may be used as indices that indicate the qualityof the read signal and that are correlated with the error rate. Itshould be noted that the error rate may also be obtained with theaverage Pave₁₀ supposed to be zero because the average is expected to beapproximately equal to zero.

The optical disk drive 100 according to the preferred embodimentdescribed above has a configuration such as that shown in FIG. 7.Alternatively, the optical disk drive 100 may further include anotherwaveform equalizer 28 having such an equalization characteristic as toallow the PLL circuit 12 to generate a clock signal more appropriatelyas shown in FIG. 10. Just like the optical disk drive 100 shown in FIG.7, the optical disk drive 100 shown in FIG. 10 can also obtain thestandard deviation and the average and can evaluate the quality of theread signal by using them. In addition, by separately providing twowaveform equalizers for shaping the waveform in such a manner as to getthe clock signal generated more appropriately and to get the read signaladapted to the PRML decoding method more suitably, respectively, apreferred read clock signal can be generated and the read signal can bedecoded by the PRML decoding method more accurately. An optical diskdrive like this, including two or more waveform equalizers, is disclosedin U.S. patent application Ser. No. 09/996,843, which was filed by theapplicant of the present application and which is hereby incorporated byreference.

As another alternative, a read clock signal may also be generated basedon the output of the A/D converter 13 (i.e., digital signal) as shown inFIG. 11. Even so, just like the optical disk drive 100 shown in FIG. 7,the optical disk drive 100 shown in FIG. 11 can also obtain the standarddeviation and the average and can also evaluate the quality of the readsignal by using them.

In the preferred embodiments described above, the quality of the readsignal is evaluated by using the standard deviation σ and average Paveof the Pa−Pb distribution, which are output from the differential metricanalyzer 16, as respective indices. Optionally, a control operation mayalso be carried out by using these indices (i.e., the standard deviationσ and average Pave) to improve the quality of the read signal. Forexample, the frequency characteristic of the waveform equalizer 11 maybe modified by the frequency characteristic controller 29 shown in FIG.12 so that the average or the standard deviation output from thedifferential metric analyzer 16 becomes zero or minimized. Then, thequality of the read signal can also be improved. Furthermore, as for anoptical disk drive that can write information on the storage medium,recording parameters can be optimized by controlling the recording poweror the degree of recording compensation (e.g., recording pulse width) sothat the average or standard deviation, output from the differentialmetric analyzer 16, becomes zero or minimized.

Embodiment 4

Hereinafter, an optical disk drive according to a fourth specificpreferred embodiment of the present invention will be described withreference to FIG. 13.

In this preferred embodiment, the differential metric analyzer 160outputs the PRML error index MLSA (M=σ/2·d_(min) ²) as defined byEquation (14). It should be noted that the PRML error index MLSA isobtained by dividing the standard deviation (or root mean square) σ ofthe most probable state transition path from the read signal by theEuclidean distance between the most probable and the second mostprobable state transition paths. The PRML error index MLSA is an indexthat can be used to evaluate the quality of the read signalappropriately when the PRML decoding technique is adopted.

As shown in FIG. 13, the error index MLSA that has been output from thedifferential metric analyzer 160 is supplied to a frequencycharacteristic controller 290. The frequency characteristic controller290 optimizes the characteristics of the waveform equalizer 11 (e.g.,the boost level and the boost center frequency thereof) so as tominimize the error index MLSA. For example, the frequency characteristiccontroller 290 may change the boost level slightly and then compare thePRML error index MLSA resulting from the original boost level with thePRML error index MLSA resulting from the slightly changed boost level.Based on the result of the comparison, the frequency characteristiccontroller 290 may select one of the two boost levels that has resultedin the smaller MLSA. By performing such an operation repeatedly, thefrequency characteristic controller 290 can optimize the characteristicsof the waveform equalizer 11 and converge the PRML error index MLSA to aminimum value.

As another alternative, the PRML error index MLSA that has beengenerated by the differential metric analyzer 160 may also be suppliedto a focus offset searcher 291 as shown in FIG. 14. In reading a signalfrom the optical disk 8, the optical disk drive 100 performs a focusservo control so that the light beam emitted from the optical head 50can always scan the information recording plane of the optical disk 8.This focus servo control is carried out by subjecting the focus actuator(not shown) of the optical head 50 to a feedback control so that thefocus error signal that has been detected by a servo amplifier 91 isequalized with a predetermined target value X0 by way of a subtractor92. In this case, the focus offset searcher 291 may output a valuecorresponding to the smallest PRML error index MLSA as the predeterminedtarget value X0 to the subtractor 92. Then, the focus servo control maybe carried out in such a manner as to minimize the PRML error index MLSA(i.e., to minimize the error rate). It should be noted that such atarget value X0 may be searched for by detecting the PRML error indexMLSA corresponding to a slightly changed target value X0 and comparingthe MLSA value detected with the original MLSA value.

In this preferred embodiment, the focus target value is optimized byusing the PRML error index MLSA. Alternatively, the PRML error indexMLSA may also be used to optimize any other servo target value. Forexample, the PRML error index MLSA may also be used for tracking servocontrol, disk tilt control, lens spherical aberration correction and soon.

Furthermore, the present invention is also applicable to an optical diskdrive including two optical heads 50 and 51 for reading a signal fromthe optical disk 8 and writing a signal on the optical disk 8,respectively, as shown in FIG. 15. In that case, the recording power maybe controlled by reference to the PRML error index MLSA that is outputfrom the differential metric analyzer 160. A signal to be written on theoptical disk 8 is generated by a write signal generator 103 and thensupplied to the signal writing optical head 51 by way of a modulator102. The modulator 102 multiplies the write signal by an appropriate,recording power P and then supplies the product to the optical head 51.In this case, the PRML error index MLSA that has been generated by thedifferential metric analyzer 160 may be supplied to a recording powercontroller 292. Then, the recording power controller 292 may determinethe recording power P in such a manner that the PRML error index MLSA isminimized.

The optical disk drive 100 shown in FIG. 15 gets the read and writeoperations performed by the two different heads 50 and 51.Alternatively, a single head may be switched to perform the read orwrite operation selectively. Also, in the preferred embodiment describedabove, the recording power is controlled by using the PRML error indexMLSA. Optionally, the width or the phase of write pulses may also becontrolled by reference to the PRML error index MLSA.

Various preferred embodiments of the present invention described aboveprovide a method for evaluating the quality of a read signal that hasbeen decoded by a maximum likelihood decoding method, in which a mostprobable state transition path is selected from a number n of statetransition paths that represent n probable transitions from a firststate at a time k−j into a second state at a time k. In this method,supposing the probabilities of state transition of the most and thesecond most probable state transition paths in a predetermined period jbetween the times k−j and k (e.g., a sum of Euclidean distances in thepredetermined period j) are represented by Pa and Pb, respectively, thereliability of the decoded result obtained in the period j is evaluatedby |Pa−Pb|. Also, by measuring the |Pa−Pb| values a number of times andby obtaining the variance of the |Pa−Pb| distribution, error indices,which are correlated with the error rate of the digital decoded resultobtained by the maximum likelihood decoding method, can be obtained asindices to the quality of the read signal.

While the present invention has been described with respect to preferredembodiments thereof, it will be apparent to those skilled in the artthat the disclosed invention may be modified in numerous ways and mayassume many embodiments other than those specifically described above.Accordingly, it is intended by the appended claims to cover allmodifications of the invention that fall within the true spirit andscope of the invention.

1. A method for evaluating the quality of a read signal that has beendecoded by a maximum likelihood decoding method, in which a mostprobable state transition path is selected from a number n (where n isan integer equal to or greater than two) of state transition paths thatrepresent n probable transitions from a first state Sk−j (where k is aninteger equal to or greater than three, j is an integer equal to orgreater than two and k is greater or equal to j) at a time k−j into asecond state S_(k) at a time k, the method comprising the steps of: (a)detecting predetermined combinations of the first and second states Sk−jand S_(k) that define the n probable state transition paths in apredetermined period j between the time k−j and k; (b) evaluating thereliability of the decoded signal, which has been obtained in thepredetermined period j, by using |Pa−Pb| in reference to Pstd, where Paand Pb are indices indicating the respective probabilities of statetransition of first and second state transition paths in thepredetermined period j, the first state transition path being estimatedto be either one of the most probable or the second most probable, andthe second state transition path being estimated to be the other of themost probable or the second most probable, among the n probable statetransition paths that are defined by the predetermined combinations thathave been detected in the step (a), and where Pstd is a sum of squaresof differences each between an ideal sample value shown by the firststate transition path and an ideal sample value shown by the secondstate transition path, wherein one of the first and second statetransition paths being estimated to be the most probable statetransition path, and the other one of the first and second statetransition paths corresponds to one-bit shift as compared with the mostprobable state transition path.